What Triggers Audio Processing?

Using the Teensy or Tympan for audio processing can be very exciting.  It's really fun to open up the example programs, compile them, and listen.  It's also pretty easy to look at the example code to see how the algorithm blocks are created and connected together.  Great!  But, what if you want to make your own algorithm?  That's when start to look a bit more critically at the examples.  Your first thought will likely be: "Wait.  How does any of this audio processing actually get called? How does this crazy structure work?!?"   Yes.  That's a good question.  Let's talk about it.

So Much is Hidden.  The essential problem is that nearly all of the audio plumbing is hidden so that its complexity doesn't scare people off.  For example, look at an extremely minimal audio processing example in the image below.  It instantiates the audio objects and creates the audio connections.  Then, you've got the traditional Arduino setup() and loop() functions.  Note that the loop() function is empty.  This program looks like it does nothing.  Yet, audio does flow.  The audio is made louder by the gain block applying 6 dB of gain.  But how?!?  I see no functions that call into the audio blocks!

What You Didn't Know That You Programmed.  The screenshot above shows the code that you know that you programmed.  There is also a whole bunch of code that you included, however, that you didn't know that you were invoking.  In effect, you programmed some very complex activities and you didn't even know it.

Going Down the Rabbit Hole.  The flow chart below tries to expose some of the hidden code.  This is a map that helps explain some of the hidden underground parts of the Teensy Audio Library (and Tympan Library). 

1) Code Shown in the Arduino Window.  The blocks in blue are the pieces of code that you know that you wrote.  This is the code shown in the Arduino IDE.  Here, you instantiate the audio classes and the audio connections.   Here, you write the Arduino setup() and loop() functions.  This is the part that we can all see and (usually) understand.  For the audio processing, the hidden magic gets invoked behind the scenes by the audio classes.  In particular, the AudioOutputI2S class is the most magical.

2) Audio Class Constructors.  As a bit of background, "I2S" is a communication system built into the Teensy processor that is purposely design to pass sound data (that's the 'S' in I2S) between the processor and the audio input/output hardware.  So, the AudioOutputI2S class handles the passing of audio data out from the processor to the audio output.  If you were to open the AudioOutputI2S class, you would see that its constructor calls its begin() method.  Looking in begin(), you'll see that it configures the I2S bus (which is logical) but it also configures the DMA and it attaches an interrupt to the DMA.  Huh?

DMA. Direct Memory Access is a special way of using memory.  You know how you can drive your car and listen to a podcast at the same time?  Your brain is able to handle certain tasks autonomously in the background without disturbing the foreground thoughts?  The processor has some of the same capabilities.  The processor can allow for certain regions of its built-in memory to be directly accessed by external devices.  In this case, DMA is configured so that the audio output system can read audio data directly from the processors memory without the processor having to respond to a request for each and every sample.  That's DMA.  It happens in the background.

3) Firing an Interrupt (ISR).  When the DMA is set up, it's pointed to a small region of memory.  The region holds a fixed number of audio samples.  Once the I2S bus is commanded to begin pumping data, it starts pulling data from the DMA.  Again, this happens in the background.  As the DMA empties, it'll get low on samples that remain.  In the DMA setup, the DMA has been configured to call a function (an interrupt service routine, ISR) to replenish the data in the DMA.  In the AudioOutputI2S begin() method, a specific function was attached as the ISR.  You didn't know it, but it was.  The ISR is right there in AudioOutputI2S.

Interrupting All Other Activities.  When the ISR is requested, the processor now has to take notice.  It is called an "interrupt" service routine because it interrupts whatever else is happening.  Whatever else the processor is doing (such as looping around in your Arduino loop() function) will be paused while the processor goes off and executes the ISR.  This interruption is done so that we can ensure there is fresh audio data placed into the DMA before the DMA fully empties and the audio stalls.

4) Execute the ISR.  Looking in AudioOutputISR, we see that the ISR copies previously-processed audio data into the DMA.  This keeps the DMA fed so that there are no hiccups in the audio.  Great.  The next thing that the ISR does is command update_all(), which starts the audio processing chain so that processed audio will be available the next time the DMA is running low.  This update_all() is the key.

Doing the Audio Processing.  The update_all() method lives in AudioStream.  AudioStream is the root (parent) class of every audio processing class that you might have instantiated in your Arduino code.  AudioStream has some static data members that, in effect, act as a central location for tracking every audio processing object that needs to be called.  Update_all() simply loops through the list of your audio objects and calls each one's update() method.  

Each Class's Update().  If you open up any audio class, you'll find that there is an update() method.  This is where all the audio processing is done.  Inside the update(), it pulls blocks of audio from its upstream connections and pushes audio blocks out to its downstream connections.  These upstream and downstream connections are known because of you created them in your Arduino code via those AudioConnection lines.

Summary.  So, that's how the audio processing happens on Teensy (and Tympan).  There is the code that you explicitly wrote and then there is all the code that comes along with the libraries, such as the class  AudioOutputI2S.  AudioOutputI2S sets up the I2S bus for passing data to the audio hardware and it sets up the DMA for feeding data to the I2S bus.  Whenever the DMA gets low on data, it fires an ISR.  The ISR refills the DMA and it launches the cascade of update()for all your audio objects.  Because it is interrupt driven, it all happens in the background...and that's why your Arduino code looks so empty.

Phew.  Good work, everyone.

Teensy Audio Board Self-Noise

When working with audio, one typically wants as quiet a system as possible -- no one likes listening to hiss.  So, when I started working with the Teensy and the Teensy Audio Board, I applied a critical ear to the board's performance.  While the Teensy Audio Board was very fun, quite easy to use, and relatively inexpensive, I found that it was noisier than I like.  In this post, I'm going to illustrate the noise levels that I recorded and I'll show a workaround that helped remove a lot of that noise.

Setup:  For these tests, I used a Teensy 3.6 attached to Teensy Audio Board.  I then wrote an Arduino sketch (shared on my GitHub here) that would record audio from the line-in and send it to both the headphone output as well as to the USB Audio output.  I recorded the digital audio coming through USB using Audacity (as discussed here).  As shown in the picture above, To try to isolate just the self-noise of the system, I shorted the inputs using a jumper across the Teensy Audio Boards line-in terminals.  This should be as quiet as it can get.

First Results:  The audio that I recorded (shared here) sounded funny to my ear.  If I turned it up, I could hear a very annoying unsteady whining noise.  Looking at the spectrum (see plot below), I could clearly see some narrowband tones starting around 2 kHz.  That's right where one's hearing is most sensitive, which makes this kind of self-noise particularly problematic.  It's definitely not what you want if you're trying to make a hearing aid type of device.  What could be the cause of this?

Disable the ADC's HP Filter:  After a bunch of messing around, I finally stumbled across this post on tthe Teensy forum.   Here, "Raj" stated that the SGTL5000 audio codec (which is at the heart of the Teensy Audio Board) has a high-pass filter in its ADC.  He said that this HP filter was introducing a lot of noise and he shared the command for disabling that filter.  When I put the command "adcHighPassFilterDisable();" into my sketch and re-ran my tests, those annoying narrowband tones in the Teensy Board's self-noise went away (audio file here).  Ahhh.  That's so much better.

Varying the Gain:  The data shown above were taken with the input gain of the Teensy board set to "10" (ie, full-scale input spans 0.56 Vpp).  There are other gain settings that one could use.  So, I repeated my measurements at other gain levels to see if the input-referred self-noise was better or worse.  The results are below.

 As can be seen, the noise with the HP filter (the blue line) is noisier in all cases than when the HP filter is disabled (orange line).  So, as long as you can handle a little DC offset in your audio data, you should definitely disable that filter.

A second finding is that the apparent (input-referred) self-noise goes down as the gain increases.  So, if you have really quiet signals that you're trying to record, turning up the gain might help reveal those signals.

Dynamic Range:  The trade-off with turning up the gain is that the maximum signal level that can be recorded without clipping also goes down as the gain is increased.  For many applications, therefore, it is just as important to look at the dynamic range for the system.  The dynamic range is the difference between the maximum input level and the noise floor.  When I run the numbers for the Teensy Audio Board, I get the results below.

Here, I see that, when the HP filter is disabled (the orange line), the Teensy Audio Board has about 81 dB of dynamic range.  And, I also see that the dynamic range is basically independent of the gain setting.

Is it Good Enough?  So now we're down to the hard question:  is 81 dB of dynamic range good enough for my needs?  Well, it is a pretty decent number, especially for the price of the Teensy Audio Board.  But, for my use as part of an open-source hearing aid, where I need to amplify quiet sounds while not distorting on already-loud sounds, I think that I need a bigger dynamic range.  Normal human hearing spans on the order of 120 dB of dynamic range.  I think that I need hardware that'll get me at least a little closer to that number.

Motivation for a New Board:  The results shown here were my motivation for building the audio interface (the "Tympan") that I introduced in my last post.  In my next post, I'll share some details of that audio interface and I'll perform these same self-noise measurements to see if I was able to get a wider dynamic range.  Making wide dynamic range systems isn't easy, so it'll be exciting to find out how I did!

Follow-Up:  I measured the self-noise and dynamic range of the new Tympan board.  It's pretty good!  If you're interested, you can see the results here.

For Speedy Float Math, Specify the Float Version

When programming up my audio processing algorithms on the Teensy 3.6, I sometimes find that the math operations are much slower than I was expecting.  Yes, some things are super-fast: arithmetic, FIR filters, FFT.  But did my code with the logarithm run so slowly?  Well, it turns out that I was using the wrong function call.  If you use the float-specific version of your function, you get tremendously faster floating-point speeds.  Don't rely on the compiler; be explicit and call it yourself!

As you can see in the graph above, I measured how long it took to complete several different math functions when using floating-point data.  The interesting part is that each math function can be called in two different ways: (1) using its generic form such as sqrt(x) or (2) using its explicitly floating-point form such as sqrtf(x).  In all cases, the explicit floating-point form was much faster.

Being a Matlab programmer, my fingers generally type out the generic form of the function.  Being naive, I had assumed that the compiler would detect my data type and automatically substitute the exact same floating-point function that I would have called myself.  Apparently, I was wrong.  Way wrong.

The table above shows that the square root function benefits the most when using the explicitly floating-point form.  The explicitly floating-point version is over 30 times faster!  The Teensy (well, every ARM M4F) has hardware acceleration for doing square roots.  I'm guessing the sqrt(x) form does not use the acceleration whereas the sqrtf(x) form does.  30x is a huge large increase in speed.

Interestingly, the logarithm and exponential/power functions do not have hardware acceleration in the Teensy.  Yet, when using the explicitly floating-point version, they see a 10x increase in speed.  Stunning.

Why are the explicitly floating-point versions so much faster?  I don't know.  But I sure as heck am going to make sure that all my future code uses them.

Tech Info: This data was measured using a Teensy 3.6 running at 180 MHz.  It was programmed from the Arduino IDE (1.6.13) via the Teensyduino (1.35) add-on.  My code is on my GitHub here.

Follow-Up:  Why is the float-specific version ("logf()") so much faster than generic version ("log()")?  I posted this to the Teensy Forum.  Their replies (here) were pretty definitive.  Under the hood, the generic version (ie, "log()") will do the calculations as double-precision floating point math, which is all in software.  By contrasts, the floating-point version ("logf()") is for single-precision floating point math, which on the Teensy is done with hardware acceleration.  That explains why the float-specific version is so much faster.

Reducing Current Draw

My previous post introduced my Teensy-based hearing aid.  While my primary goal was to make a platform for developing audio processing algorithms, I am interested in exploring its performance as an actual hearing assistive device.  From this viewpoint, battery life is important.  In assembling my device, however, I gave no thought to minimizing power consumption.  Does it draw too much current?  Will it have a usable battery life?  Let's find out!

Initial Measurements:  With my baseline Teensy Hearing Aid, I measuring the current being drawn from the battery during normal operation.  At this early stage of development, the Teensy isn't doing very much -- it is simply applying digital gain to the audio stream.  Because it is doing so little, I am hoping that we'll see the lowest power consumption.  My results are below.  Note that I measured the power consumption across a range of processor speeds.  You can set the speed of the processor via the Arduino IDE when you compile the sketch.

That's A Lot of Current!  I was surprised to find that at its normal speed (180 MHz) the system was drawing almost 91 mA of current.  That's a lot of current.  My battery has a capacity of 350 mA-hours, so my battery life will only be about (350 mA-hrs / 91 mA) = 3.8 hours.  For a "hearing aid", this is pretty short.  Yes, I could slow down the processor to reduce my power consumption, but this is an inelegant solution that requires me (the programmer) to ensure that my software will always live happily within the limits of the slower speed.  I'd prefer a more dynamic approach, where the code itself will switch between low-power and high-performance modes as the workload demands.  I don't know how to do that.

Sleep During Idle:  Luckily, I have a friend who is experienced with low power embedded systems.  He suggested that I could save a lot of power by putting the processor to sleep during idle periods.  Knowing that I'm working with an ARM processor (the heart of the Teensy board), he suggested that I insert the ARM-specific command asm(" WFI") into my main loop (yes, you do need the space before the W).  When the processor hits this command, it'll go to sleep and consume less power.  It'll stay asleep and "Wait For Interrupt" (hence "WFI") before waking to resume its work.

Wait for Interrupt:   Since I don't want it to sleep forever, I need to make sure that there is an interrupt (such as a timer) that'll wake the system periodically so that it can do its work.  As I don't know how to do this, I have a problem.  Luckily, I know that the Teensy Audio Library already uses interrupts to do its work.  I know that it fires at least one interrupt every 128 audio samples.  As any interrupt will trigger the WFI to wake up, I don't need to do anything more.  I can just add the WFI command and rely upon the Audio Library to wake the system.  The system will automatically go back and forth between sleep and wake.  One line of code -- what a simple solution.

It Works!  After adding the WFI command (my code is here), I measured the current draw again.  The WFI command works!  At the default speed of 180 MHz, the system now draws only 57 mA, instead of 91 mA as seen before.  That's a 34 mA savings with no impact on system performance.  Fantastic.

Battery Life:  By adding the WFI command, power consumption has dropped to 2/3 of its original value.  My system will now have 50% more battery life.  Using my 350 mA-hr battery, I'll now get 6 hours of life instead of 4 hours.  That's a great improvement for adding just a single line of code.

More Power Savings?  While increasing my battery life by 50% is great, I went back to my friend asking if more savings could be had so easily.  He said that I could save more power, but not nearly as easily.  He said that the next step would be to identify and disable peripherals that I don't need.  But, to do this, I'd have to read through and understand my processor's datasheet, which is not an easy task for a newbie such as myself.  So, for now, I think that I'll be content with the easy savings provided by the WFI command.

For Fellow Nerds...My Raw Data:  For anyone who is really interested, my raw data is in the table below (or here).  It is interesting that, even at very slow processor speeds, I still see power savings when using the WFI command.  Clearly, my "Gain Only" audio processing algorithm requires very little effort from the processor.  That Teensy 3.6 sure is fast!

A Teensy Hearing Aid

Hearing aids are totally closed devices -- their inner workings are hidden.  Access is limited to only those who work for the hearing aid companies.  But if innovation is to accelerate, we need more ideas iterated more quickly.  We need more people to participate in hearing aid development.  But if the devices are closed, there is no way to try new ideas.  So, let's consider the alternative.  Let's try to build an open-source hearing aid.  Yes, at first, an open-source hearing aid will be absurdly big and ugly.  But, you have to start somewhere.  I'm going to start here: take one Teensy microcontroller, add some supporting electronics, and VOILA! A Teensy Hearing Aid!

Basic Hearing Aid Elements:  While it is unfortunate that they are closed devices, real hearing aids are absolutely amazing pieces of technology.  Their minuscule packages are absolutely stuffed with functionality.  I, though, am going to start more simply.  I will start with some microphones, analog and digital converts, a digital audio processor, some speakers, and a battery.  Once this works, I can always add more features later.

Choosing a Processor:  For me, the biggest challenge is always with the software.  Therefore, I need to choose a digital audio processor that it is easy to program.  For me, that means choosing a processor that can be programmed from the hobbyist-friendly Arduino programming environment.  Within that universe of processors, I've chosen to use the Teensy 3.6 because it's fast and because it has a nice audio processing library to make it even easier to program for audio.

Supporting Elements:  To get audio signals into and out of the processor, the Teensy folks offer an inexpensive Audio Adapter Board that mates directly to the Teensy 3.6.  It has the audio ADC and DAC that I need.  For the microphones, I'm using a pair of mic breakout boards from Adafruit.  For speakers, I'm using whatever headphones or earbuds that I might have on-hand.  Finally, for the battery, I'm using a Li-Po battery and Li-Po charger from Adafruit.

Wiring It Up:  The figure above gives an overview of how everything was connected together.  As you can see, the Audio Board is at the center with everything else connecting to it.  The only tricky part of this setup is connecting the battery and charger into the Teensy system.  As indicated on the Teensy pinout diagram, you have to cut a trace on the backside of the Teensy so that you can insert the battery connections.  Once cut, the Teensy's 5V USB voltage goes to the battery charger and the battery's output goes back to the Teensy's "5V" input pin.  Not too bad.

Initial Software:  While this post is primarily about the hardware, I did write some basic software in order to see if the hardware is working (see my GitHub repo).  I used the Teensy Audio Library to configure the Audio Board to pass the "I2S" inputs (ie, my microphones) to the "I2S" outputs (ie, my headphones).  In between, I wrote a simple routine that applies a user-controllable amount of gain to make things louder.  I use the blue potentiometer on the Audio Board to set the amount of gain.

First Audio:  Of course, the first time that I tried to compile the code, my software didn't work.  Does anyone's code ever work the first time?  After some iteration, I finally got it to compile and upload.  Putting on my headphones, I could hear the audio being picked up by the microphones.  Turning the blue pot, I could control its volume.  Hardware knobs are so satisfying.  My favorite part, though, is being able to use the on-board battery so that I can move around freely.  Very fun.

Limitations:  Sure, my home-brewed "hearing aid" is ridiculously large -- no one (including me) would ever wear this around in everyday life.  But, unlike commercially-available hearing aids, my device is open.  Anyone can modify it to make it better.  Anyone can try out their own audio processing algorithms to try to improve one's hearing.  Will any of us beat the professional hearing aid algorithm designers?  Probably not.  But, for me at least, I will surely learn a lot by trying a few of the standard approaches.  And, I'll get to look really cool sharing pictures of myself with this (not so) Teensy Hearing Aid.  Happy hacking!

Follow-Up:  I measured the power consumption of my Teensy Hearing Aid.  Using the "WFI" command, I found a super-easy way to increase the battery life by 50%.  Wow!  See my post here.

Follow-Up:  I measured how the volume control affects the headphone ouput.  See here.

Teensy Audio over USB

In my last post, where I sent my first analog audio through a Teensy, I also discovered that it has the ability to exchange digital audio over its USB link.  Whoa.  This means that, if I'm developing some snazzy new audio-processing algorithm, I can test it 100% digitally without adding any complications of converting back and forth through analog signals.  That is a really powerful capability that'll greatly simplify my audio development.  Let's see if it really works!

Discovering USB Audio:  I only discovered that the Teensy might be able to do USB Audio while using their web-based graphical tool.  This is a tool that the Teensy folks ahve created to help people work with their Audio Library.  While using that tool, I noticed that there were input/output blocks named "USB".  Does this mean that Teensy can exchange audio over USB?!?  Really?  That's a pretty advanced feature for an electronics board aimed at hobbyists!  Does it work?

A Simple USB Audio Chain:  To give it a try, I configured an audio chain as shown below: one stereo USB input connected to one stereo USB output.  The left channel is just connected straight across -- no processing.  For the right channel, though, I've inserted a Biquad filter block just so that I can confirm that the Teensy is indeed doing something to the audio.  It's a pretty simple setup.

It Didn't Work:  When I exported the audio chain above, loaded it onto the Teensy, and gave it a try, it didn't work.  I got silence.  I don't know why.  So I started messing around...

Making it Work:  To get the USB Audio to work, I found that I had to engage the audio board's hardware in some way.  One way to make it work is shown below: add a SGTL5000 block for the Audio Board, and add an I2S block to be the output of the Audio Board.  I connected the I2S output to be just like the USB output.  Now, whatever the Teensy is sending out via USB will also be present at the headphone jack.  Sure, it seems like an unnecessary complication if I just want to use USB for my audio, but it's kinda cool that it's so easy to output to multiple targets simultaneously.

Completing the Arduino Code:  The graphical web-based tool shown above doesn't produce a complete program to load onto the Teensy -- it just gets you started.  When I hit the "Export" button, it gave me all of the code to setup the hardware and make the connections, but I still needed to write the last bit of code to make it run.  As usual, I did my coding in the Arduino IDE because it's easiest.

My Code:  The screenshot below shows the Arduino sketch that I used for this demo (it's on my GitHub here).  At the top is the big block of code that was exported from the web-based tool.  Easy.  Then, at the bottom, I added the setup() and loop() functions.  As you can see, the setup() function configures the SGTL5000 audio board and it sets the biquad filter to be a low-pass filter at 500 Hz.  The loop() function does nothing.

Tell the Compiler about USB Audio!  The only trick to using the USB audio is that you need to tell the compiler that you want the Teensy to run in USB Audio mode.  So, prior to compiling and uploading this Arduino sketch, go under the "Tools" menu, click on "USB Type" and select "Audio".  Notice that there are many other choices, including "Serial", "Keyboard, "MIDI", "Audio" and "No USB".   Normally, one uses "Serial" so that Serial.println() is able to print messages to the Serial Monitor.  But, for this demo, I want "Audio".

Loading onto the Teensy:  Once you change the USB setting to Audio, you can compile and upload to the Teensy.  The first time you do it, it'll probably upload to the Teensy without any issue.  Great!  But, once it is in USB Audio mode, future programs won't appear to upload automatically.  Why?  Well, once the USB link set for Audio, the Teensy can't get reprogramming commands over that same USB link.  What's the solution?  After the Arduino IDE has finished compiling, simply press the Teensy's reset button (picture below).  After a reset, the Teensy knows to check in with the PC prior to switching over to Audio mode.  It will automatically get any new program waiting for it.  It's a small extra step, but I didn't find it to be a problem at all.

Testing Using Audacity:  Once the Teensy is in USB Audio mode, the Teensy appears to your PC as if it is a soundcard.  So, you can now send and receive audio data to it using any audio recording program.  For this demo, I used Audacity because it is free.

Configuring Audacity:  With the Teensy attached, my computer now has two soundcards: (1) its built-in soundcard and (2) the Teensy.  Once Audacity launches, I configured Audacity to use the Teensy as the soundcard instead of the built-in one.  The screenshot below shows the five settings that I changed in Audacity.  On my computer (Windows 7), the Teensy cryptically appeared as "Digital Audio Interface (2-Tee" [sic], which wasn't as quite helpful as informative as it could have been, but it was good enough for me to choose the right item.

First USB Audio:  For this test, I'm want to send audio out over USB (to the Teensy) and record audio coming from USB (from the Teensy).  So, I need to start by creating a test signal to send out over USB.  Under the "Generate" menu, I chose "Chirp" and made a linear frequency sweep from 100 Hz to 4000 Hz.  This appeared as a single mono track in Audacity.  That's all the preparation that I needed to do.  Now, I simply hit the red record button.  Audacity started playing out the chirp audio to the Teensy while recording the audio coming back from the Teensy.  The result is shown in the screenshot below.

Success!  The screen shot shows two audio files.  Both files are shown in "spectrogram" view (60 dB dynamic range).  The top file contains the original (mono) frequency sweep generated by Audacity.  This is what was sent to the Teensy over the USB Audio link.  The bottom file shows the stereo audio recorded from the Teensy.  The left channel had no processing being performed by the Teensy and it does indeed appear to be a copy of the original signal.  The right channel, though, was being processed by the Teensy by its 500 Hz low-pass biquad filter.  As can be seen, the high frequencies are attenuated -- the gentle roll-off is as expected from a biquad filter.  This was amazingly easy!

Future Use:  While I'm very impressed that this capability exists at all, it's not perfect.  In additional testing, I occasionally found hiccups or other artifacts in the audio stream coming back from the Teensy.  But, most of the time, this USB Audio link worked really well.  It'll be great for debugging my audio projects.  Anytime I have any question about the negative effects of my analog components, I can simply switch over to USB Audio to avoid the whole problem.  It'll be a great tool to have in my audio hacking toolbox.

Teensy Audio Board - First Audio

After having good success with the speed of the Teensy products for doing audio-relevant operations, I've decided that it's now time to start playing with actual audio signals.  To do this, I need some sort of interface for getting analog audio signals into and out of the Teensy.  Luckily, Teensy makes an audio board just for this purpose.  Today, I'm going to give the Teensy Audio Board a try.

Buying The Parts:  The first step of a new project is always fun: buying the parts.  I go to Adafruit or Sparkfun, I see what they have in stock, and I order all the stuff that I need.  This is the part of the project where the vision and dream fills one with excitement, without being tempered by any of the actual hardware and frustration that comes with building and trouble-shooting.  And if that wasn't good enough, in a few days, you get a box full of shiny things!

For this project, I used a Teensy 3.2, a Teensy Audio Board, some 14-pin female headers for the Audio Board, a 10K pot to fit into the "volume knob" spot on the Audio Board, and a 3.5 mm stereo audio jack.

Assembling the Audio Board:  This part of the project was pretty straight-forward.  Simply solder on the female headers, solder on the 10K pot, and solder some wires between the "Line-In" holes on the Audio Board and the 3.mm audio jack..  As you can see in the photo below, I could have done a better job with the audio jack, but it's good enough for this project.  (And thanks to Ray for giving it a nice sturdy plastic base!)

Assemble with the Teensy:  After finishing the assembly of the Audio Board, I turned to the Teensy itself.  All that is needed is to solder on some male pin headers.  Then, the Teensy can be connected to the Audio Board.

Audio Software:  To use the Teensy with the Audio Board, you some software that tells the Teensy how to interact with the Audio Board.  Because audio programming can be tricky, PJRC (the Teensy folks) have written a pretty extensive audio library.  It's pretty impressive.  I chose to use this library for my initial trials.  You can get the library from their GitHub repo (as described here) or, even easier, it was probably already installed on your computer when you first installed the drivers for the Teensy itself (via the "Teensyduino" installer).

Audio System Design Tool:  The hardest part of doing something new is getting started.  Where do I begin?  Well, PJRC knows that this is a hurdle, so they help you get started by providing a web-based GUI for configuring your audio processing.  The idea with this GUI is that it will help you build your software for the Teensy.  The Teensy doesn't know about the Audio Board -- you have to tell it everything.  So, as you can see in the screenshot below, I started by dragging in a module called "sgtl5000".  The SGTL5000 is the audio codec at the heart of the Teensy Audio Board, so by using the module, the Teensy will now know about the Teensy Audio Board.

Line-In Pass-Through:  The next step is to configure the audio path that I'd like.  For this demo, I simply want to pass audio from the Line-In input to the headphone output.  From the Teensy's perspective, the Audio Board will provide these signals to the Teensy over the Teeny's I2S bus.  So, in the GUI, I  dragged in an I2S input module and I dragged in an I2S output module.  Finally, I drew lines connecting the inputs to the outputs (the two lines represent the left and right audio channels).  And that's it!

Exporting to the Arudino IDE:  This GUI is merely a tool to help you get started with configuring your audio processing chain.  It doesn't compose all of the software for me.  Instead, I need to export this audio configuration and get it into the Arduino IDE, where I can complete the programming and put it on the Teensy.  So, I clicked on the GUI's "Export" button, at which point it pops up a window with a bunch of Arduino code ready to be copied-and-pasted into a new Arduino sketch.

The GUI-Provided Arduino Code:  The figure below shows a screen-shot of my completed sketch in the Arduino IDE.  The first part of the sketch is the code provided by the web-based GUI tool.  This code imports the required libraries, instantiates the required audio-related objects, and connects them together per the drawing that I made in the GUI.

Completing the Software:  The second half of the program is the code that I had to write myself.  I had to write the "setup()" and "loop()" functions that are the core of every Arduino sketch.  As you can see in my "setup()" function above, I do a couple of things: (1) I allocate some memory for the audio library to use and (2) I issue a few commands to configure the settings within Audio Board.  I stole all of this code from example programs in the Audio library.  After the "setup()" function, I wrote the "loop()" function.  Based on the example code, I don't need anything here.  Once properly configured, the Audio Library handles everything in the background.  My code is on my GitHub here.

First Audio Testing:  For my first audio test, I simply want to inject an audio signal into the Teensy and record the audio signal that it produces in response.  Since the Teensy was programmed to pass the audio through without any manipulations, the output should be the same as the input.  Let's see!

Setup:  I compiled the code and loaded onto the Teensy.  To generate a test signal, I used my computer.  I used Audacity to make a linear frequency sweep (a "chirp") and played it out of the computer's headphone jack.  I connected the headphone output of my computer to the Line-In jack on the Teensy Audio Board.  I recorded the audio output of the Teensy Audio Board by connecting its headphone output to a Roland R-05 handheld audio recorder that I happen to have.  I hit record on the Roland and I hit play in Audacity and, like MAGIC!, I found that I had audio passing through the Teensy.   Yay!

First Data:  After recording the audio chirp with the Roland, I transferred the audio file over to the PC and opened it in Audacity (available here).  As can be seen in the screen shot below, it does indeed look like a chirp, which is good.  I also see, however, that it is not a pure chirp signal -- I see some unexpected lines in the spectrogram.  To me, these spurious lines look like harmonic distortion and some sort of aliasing.  These undesirable signals are not very loud compared to the primary signal, but they are clearly present.  So, while I'm pleased with my initial success with getting this Teensy-based audio system to work, I also see that there is some work ahead to optimize the audio quality.

Next Steps:  My next steps are to investigate other features of the Audio library (the audio library provides for USB-based audio transfer!?!  That's pretty advanced!) and to try the Audio Board with the Teensy 3.6 instead of the Teensy 3.2.  There's fun times ahead with audio hacking!

Follow-Up:  I made my own Teensy Hearing Aid using a Teensy and a Teensy Audio Board.  It's fun!

Benchmarking - Teensy 3.6 is Fast!

Fast but easy to program --  that's what I need for my audio processing projects.  In my previous post, I loved the speed of the NXP K66 processor, but was frustrated with the NXP development environment.   Well, thanks to PJRC and Kickstarter, the solution has arrived...via US Mail.  Welcome to the new Teensies!  Based on my tests, it looks like audio hacking just got a whole lot more fun.

Teensy?  Teensy is a line of microcontroller boards that are much more capable than the standard Arduino boards, but that can still be programmed using the friendly Arduino development environment (the "Arduino IDE").  I've used one of the existing Teensy boards (Teensy 3.2) on a number of projects and it definitely achieves its goal: it's a powerful, fast little board that is really easy to program.

New Teensies!  Through just-completed Kickstarter, Teensy has expanded its line of boards by adding the Teensy 3.5 and Teensy 3.6.  As can be seen in the table below, the Teensy 3.5 and 3.6 have a faster clock speed and have more RAM.  The specs on the Teensy 3.6 match by my loved-and-hated FRDM-K66F board from NXP.  The increased capabilities of the Teensy 3.5 and 3.6 relative to the older Teensy (and relative to Arduino) should really help in computationally-heavy tasks, such as processing audio.

Floating-Point Prowess.  For me, the best feature of the new Teensies is the inclusion of a floating-point unit (FPU), which will accelerate calculations with floating-point numbers.  This will makes it much easier to hack together audio processing algorithms.  I loved the performance of the NXP FRDM-K66 board because its FPU made it stunningly fast on floating-point FIR and FFT operations.  I'm hoping that the Teensy 3.6 is able to match the speed of the FRDM-K66.  If it can, I can leave behind the FRDM-K66 board and never again have to struggle with NXP's development environment.

Programming the New Teensies.  To evaluate the new Teensy boards, I'm going to re-run my FFT benchmark tests (on GitHub here).  First, I had to get the latest "Teensyduino" software from PJRC (to get support for the new boards into the Arduino IDE).  Then, I simply opened up my FFT benchmarking sketch and recompiled.  It was previously written for the Teensy 3.2 and now, without any changes, it compiled successfully for the Teensy 3.5/3.6.  This is the ease-of-use that I was hoping for!

Speed Results.  I ran my bechmarking tests on the new boards and complied the results in the table below.  It shows how many FFTs each board could complete per second.  It's my raw data.  It is hard to see the interesting trends in this table, so just go ahead and jump over it...I'll present something simpler in a moment...

Which Board is Fastest?  Below is a bar chart comparing the speed of each board for a 128-point FFT.  I shows the speed when using Int32 data types and when using Float32 data types (the two most likely used in audio processing).  Two results stand out:

• The Teensy 3.6 is the overall winner, even beating the FRDM-K66F.  While that is a bit inexplicable, it's great!
• The Teensy 3.5 and 3.6 are great for floating point calculations.  Look at how big those red bars are!  Clearly, the FPU in these newer boards makes a huge difference.

How Fast Do I Need?  So the bars in the graph above are big.  How do I know what bars are big enough?  How do I know which are fast enough for audio processing?  Well, like in my previous post, I want to know which boards can keep up with calculations that need to be done at audio rates.  In this case, I want to know which boards can do FFT operations at audio rates.  What does that mean?

FFTs for Audio Processing.  FFTs are interesting for audio because it means one can process audio in the frequency domain, which can be very convenient.  To do frequency-domain processing, you need to do an FFT to get into the frequency domain and you need to do an IFFT (which is basically the same computational load as an FFT) to get back out of the frequency domain.  Then, because of windowing and other blah-blah-blah, you generally overlap your audio data blocks by 50%, which means that each audio block needs four FFT-like operations.  Can this get done in real time?

Keeping up with Audio.  Because I measured how many FFTs each board can do per second, I can estimate the maximum audio sample rate (samples per second) that each board can support while still doing four FFTs per data block.  A typical sample rate used for audio is 44 kHz.  My results below show which boards can sustain at least 44 kHz (shown in green) versus those that cannot (shown in red).

Integer vs Floating-Point Results.  As can be seen in the table, the Teensy 3.2 is fast enough for audio if I'm using integer data types (Int16 or Int32).  It is not fast enough to use Floats.  The new Teensy 3.5 and 3.6 are faster than the Teensy 3.2, especially on Floats.  The Teensy 3.6 just screams on Floats -- it has enough processing power to sustain a sample rate over 300 kHz for frequency-domain processing.  Wow.  This is exactly the result that I was hoping to see.

Conclusion.  For my audio processing projects, it looks like the Teensy 3.6 is the best choice.  It's really fast, yet it can be easily programmed through the comfortable and friendly Arduino IDE.  I'm very pleased.

Next Step:  My next step is to join the Teensy 3.6 to an audio interface (such as the Teensy Audio Board) so that I can leave these synthetic benchmarks behind and start playing with actual audio.  It's gonna be fun!

Extra Credit:  How much faster are the new Teensies vs the Teensy 3.2?  The Teensy 3.6 is 16x faster than the Teensy 3.2 on Floats.  Dang, that's fast.  Again, this must be due to the FPU in the new units.

Follow-Up:  I made my own Teensy Hearing Aid using a Teensy 3.6 and a Teensy Audio Board.  It's fun!

Benchmarking - FFT Speed

My goal is to find a good microcontroller board for doing audio processing.  Speed is a very important concern so, in my last post, I looked at the speeds for different boards when doing FIR filters.  While time-domain FIR filters are an important audio processing task, I am also curious how suitable these boards are for frequency-domain processing.  In other words, I need to know how fast they can do FFTs.  Let's find out!

Why FFT?  An FFT is a "Fast Fourier Transform", which is not a helpful name if you're not already familiar with the idea.  FFTs are most often used when one wants to look at the frequency content (the spectrum) of audio data.  Intriguingly, you can also do an inverse FFT (an "IFFT") to convert that frequency spectrum data back into audio data.  By pairing the FFT with the IFFT, therefore, one can now manipulate (or mangle!) audio data in the frequency domain, which can be a more natural and easy way to construct one's audio processing algorithms.  They key to it all is the FFT (and its computationally similar IFFT).

Microcontroller Boards:  To understand which hardware might be capable of this frequency domain approach to audio processing, I'm evaluating a range of different boards.  In addition to spanning a range of clock speeds (16 MHz - 180 MHz), they also vary in other computationally important ways:  one is 8-bit while the others are 32-bit, some have DSP extensions while others do not, and one has a floating-point unit (FPU) while the others do not.  Though my testing, I'll see what's important.

My Test Software:  For all of the boards except for the FRDM-K66F, I used the Arduino IDE to write my test software.  It's a simple program that does an FFT on dummy data of a given length.  The program uses Arduino's "micros()" command to measure the time to complete a fixed number of FFTs.  Easy.  For the FRDM-K66F board, which cannot be programmed from the Arduino IDE, I had to use NXP's IDE (Kinetis Design Studio).  The FFT functions were identical, however, regardless of which IDE I used.  All of my software is available on my GitHub (for Arduino, for Kinetis).

KissFFT Function:  The only difficult part of the software is the FFT function itself.  Since I wanted to test across a variety of hardware, I wanted to start with an FFT routine that was written in generic C.  From the FFTW website, I found an interesting comparison of different FFT routines.  From their list, one of the most generic routines appeared to be the "KissFFT".  After downloading it, I refactored the KissFFT code to enable different data types (Int16 vs Int32 vs Float32) and to remove the dynamic allocation of memroy via malloc().  With these changes, it was much more suitable for use on a microcontroller.

Raw Results:  The raw results of my speed tests are here, from which I made the summary table shown below.  The table shows the number of FFTs per second that each board could complete.  I performed the tests for different data types (Int16, Int32, Float32) and for different FFT lengths (N=32 to N=512).  This table is too dense to read, so let's skip ahead.

Speed vs FFT Length:  First, let's look at the overall flow of the data.  The plot below shows the FFT speed for different FFT lengths.  For FFTs using more data points, I would expect slower performance.  This graph confirms that expectation.  Good.  This graph also shows that the relative ranking of the different boards is the same, regardless of the length of the FFT.  This allows me to greatly simplify the rest of the plots.

Speed for Integer Data:  As the length of the FFT doesn't matter for the relative rankings, I chose to focus on an FFT size of 128.  I chose this value because, when operating on audio data sampled at 44100 Hz, N=128 yields a frequency resolution of 344 Hz, which is a reasonably useful value.  The graph below compares the speeds of the different boards for doing 128-point FFT on Int32 data.  The Arduino Uno didn't have enough memory to complete this test, so it is excluded.  Otherwise, I see that the Arduino M0 is the slowest and that the FRDM-K66F is, by far, the fastest.  The only surprise in this data is the slowness of the Arduino M0.  It is much slower compared to the Teensy or Maple than is expected based on their relative clock speeds.  My data shows that Teensy can do ~4x the number of FFTs even though its clock speed is only ~2x higher.  Clearly the M0 is not optimized for these kinds of calculations.

Can They Do Floating Point?  For audio processing projects, I hope to do all of processing using floating point data types (Float32).  Being able to utilize floating point math (Float32) instead of fixed point math (Int16 and Int32) makes the algorithms much easier to design, debug, and optimize.  The difficulty is that microcontrollers tend to be very slow with floating point calculations.  So, let's do some tests with Floats and see if any of my boards are fast enough.

FFT Speed for Float32:  The graph below shows the FFT speeds that I measured using Float32 audio data.  As can be seen by the red bars, the M0, Maple, and Teensy are very slow on Floats.  They can only do 1/3rd as many Float32 FFTs and they can Int32 FFTs.  That is a major speed penalty.  The major exception to this trend is the FRDM-K66F.  It is actually faster using Float32 than Int32.  Presumably, this is due to the float-point unit (FPU) included in the K66F chip.  Even with the FPU, I did not expect it to be faster on Floats than Ints.  Very surprising.

DSP Acceleration:  Because an FFT is such a common digital signal processing (DSP) task, some processors include internal features to accelerate this kind of math.  The Teensy 3.2 and the FRDM-K66F are both based on the Arm Cortex M4 processor core.  The Cortex M4 includes DSP acceleration.  I learned that I can invoke the ARM's DSP accelerators by calling the FFT functions from ARM's "CMSIS" library.  It took me some effort to figure it out, but I eventually got it to work.  And, boy, did it work well...

FFT Speed Using CMSIS:  My results using the CMSIS library are shown below.  Using the CMSIS routines (and the underlying hardware acceleration) really speeds up the FFTs.

The effect of the CMSIS / DSP accelerators is so dramatic that I quantified the improvement in the table below.  The speed improvement is different for the different data types.  Using Int16 data, the CMSIS routines are 4-5x faster than the Generic C "KissFFT" routines.  Wow.  For the In32 data, CMSIS is 3x faster and for Float32 data, CMSIS is 2x faster.  This extra speed is definitely a good reward for the effort spent to figure out how to use the CMSIS library.

How Fast is Fast Enough?  I want to know which boards are fast enough to enable frequency-domain processing of audio signals.  As I discussed earlier, frequency-domain processing requires that I perform an FFT to get into the frequency domain and then an IFFT (which takes the same amount of time as an FFT) to get back out of the frequency domain.  Given my measured FFT speed values, I can estimate the maximum audio sample rate that each board can sustain:

max_sample_rate_Hz = (FFTs_per_second * N_FFT / 2) * (1 - overlap)

In this equation, the "2" accounts for the need to do both an FFT and an IFFT.  The "overlap" term accounts for the fact that most people do frequency-domain processing using blocks of audio samples that overlap by 50% (0.5) in order to smooth out any artifacts at the ends of the audio blocks.

Maximum Sample Rate for Frequency-Domain Processing:  Using this equation, assuming an N=128, and assuming an overlap of 0.5, the table below shows the maximum sample rate that each board can support for frequency-domain processing.  I've highlighted in green those boards that can sustain this kind of processing at sample rates appropriate for audio (ie, greater than 44100 Hz).

Conclusion:  If my goal is to do frequency-domain processing using Float32 data, only the FRDM-K66F is fast enough.  That is my primary conclusion.  My secondary conclusions are that, if I use Int32 data, the CMSIS acceleration means that the Teensy 3.2 is a viable option.  Furthermore, if I can tolerate Int16 data, I can choose from the Maple, Teensy, or K66.  But I don't want to do that.  I want to use Floats.  So, the K66F is for me.

Looking Forward:  While the FRDM-K66F board is very powerful for doing FFT operations, it is difficult for me to program.  I prefer the simplicity of the Arduino IDE, yet the FRDM-K66F is not supported by Ardiuno.  Looking forward however, the folks who do Teensy are about to release the "Teensy 3.6", which uses the same (or similar) processor as is used in the FRDM-K66F.  Since Teensy is programmable from the Arduino IDE, I am hoping that we'll soon have the power of the K66F combined with the ease-of-use of the Teensy.  That will be a truly winning combination for open source audio processing.