Audio Signal Processing for Music Applications

I’d like to recommend this excellent—and free—online course:

Audio Signal Processing for Music Applications
by Prof Xavier Serra, Prof Julius O Smith, III

The brief: In this course you will learn about audio signal processing methodologies that are specific for music and of use in real applications. You will learn to analyse, synthesize and transform sounds using the Python programming language.

This is the second session of the course, which will start on September 21, 2015. Enrollment is open here:

I took the first session last fall. My primary motivation was to try a MOOC (Massive Open Online Course), and I wanted to pick a topic I already had knowledge in, to better evaluate the experience. For me, this topic was one in which I had an idea of the basic techniques used, but not the details and no practical experience, so it was a good fit. Plus, the course requires the use of Python, which I had interest in and wanted an excuse to learn.

Professor Serra delivers the course videos, and does an excellent job—clear and well-paced. The course helps to give a better understanding of musical components of sound, and the techniques used to alter individual aspects (especially pitch and duration, independently).

The ten-week course is not easy, and requires at least a few hours per week—a relatively small percentage of the large number of enrollees completed the course with a passing grade (yes, I passed). It requires a relatively modest amount of programming, as the sms-tools package handles most of the work, but will be tough for non-programmers. However, you can watch the videos even if you do not wish to do the weekly assignments and quizzes. The assignments will give you a much better understanding, of course.

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Dither—The Naked Truth video

This video presents the “naked truth” on dither and truncation error, by stripping away the original signal of a musical clip and listening at different bit levels. I boost the error to a normalized audio volume for easy comparison of sound quality between different sample sizes, so your listening environment is not critical, but headphones will be a plus.

Posted in Digital Audio, Dither, Video | 1 Comment

Dither widget

This is the widget I used for the animated dither chart in my Audio Dither Explained video. “Run” animates the dither process, otherwise it changes only when you change the amplitude setting. “Connect” connects the dots; this is simply a visual aid, making it easily to follow the sequence of samples.

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Audio Dither Explained video

This video discusses the how and why of dither.

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More about source code

I was admonished (in not a nice way—not terribly rude, but quite to the point that I don’t know what I’m doing) by an anonymous visitor, who concluded that I don’t know much about C++ and maybe should have written it in a different language (why, when the purpose is to give people C++ code?). I would reply to him if he had left a real email address, but maybe I should make a few things clear to all.

I supply bare bones code. I try to leave out anything not necessary, and avoid even fairly obvious optimizations (and some less obvious that would make the code more difficult to understand. For instance, the wavetables could be one sample larger and let you avoid testing for wrap-around and the resulting branch). See About source code examples.

There is a common misconception that if your class is suitable for subclassing, then the destructor must be declared virtual. This is not true. If it were, the C++ architects would have simply built it in.

So, to some (including the anonymous commenter), it may seem confusing that I don’t declare destructors as virtual, which they might conclude to imply no subclassing, while declaring variables as protected (not private), implying support for subclassing. There is a method to this apparent madness: First, I don’t expect that the object will be subclassed by you, and I want to keep it efficient. So, I don’t declare destructors virtual, which would create some overhead we don’t need. However, if you do choose to subclass, then it’s important that you have access to certain variables, hence the protected declarations where appropriate.

However, that fact is that base class destructors need not be virtual when subclassed—that’s a requirement only if you want to delete them via the base class. By not declaring them virtual, we get the lack of vtable in the typically case (of no subclasses), while still allowing subclassing.

Also, I don’t mess with namespaces, and avoid templates even though they would be useful—again, trying to focus on the code that implements the DSP algorithm. I try to fit as much of the pertinent code on the screen for you as possible, so while I like comments in my code, I keep them brief.

And I don’t go through and declare every non-changing variable as const. This is not open source code. I’m not trying to protect you or some group you are working on code with from yourselves. I’m giving you seeds, not a framework, and it’s not in a Git repository. If I keep it simple enough, I figure you’ll be able to pull the bits out that matter for you into your own code. I don’t have time for both open source and tutorials—you can find a ton of open source oscillators, filters, and modulators on the internet, and I think you’ll find that the authors do not teach you how and why the code works. The latter is few and far between, and that’s why I’m here.

I’m open to suggestions, but realize that I do think about my choices, even if it’s not apparent. So, please, let’s make it a discussion. And the anonymous fellow is invited to point us to his contributions to the public. 😉

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Pole-Zero placement v2

Pole mag
Pole angle
Zero mag
Zero angle
Sample rate (Hz)

A new pole-zero calculator

An JavaScript remake of the old Java-based pole-zero placement applet—visit that page for tips on pole-zero locations for standard biquads. The main additions are input fields for precision pole-zero placement, and an option to display the response with a log frequency scale.

The basic idea is that poles blow, zeros suck. Think of poles as controlling a frequency-dependent feedback or resonance—the impulse response of a pole inside the unit circle decays, while one outside is like runaway feedback (think of a mic feeding back into a loudspeaker). A pole on the unit circle gives a sustained oscillation (but watch out for numerical errors—keep your poles inside the unit circle, typically). Zeros absorb a particular frequency; when on the unit circle, they absorb the corresponding frequency completely.

So, poles push the frequency response up around their corresponding frequency, and zeros pull down around theirs. Keep in mind that the frequency response graph is normalized, just as the filter coefficients are. So, while a pole pushes up the response, it appears as though all other frequencies are being pushed down instead. Of course, normalization is important in practical application, but be aware of it when visualizing how poles and zeros interact.

Posted in Biquads, Digital Audio, Filters, IIR Filters, Widgets | 7 Comments

Biquad calculator v2


Sample rate (Hz)
Fc (Hz)
Gain (dB)

Here’s an update of the biquad calculator. It adds one-pole highpass and lowpass filters, and frequency, Q, and gain sliders. The sliders cover the range of typical audio settings, and are valuable for getting a quick feel for how the filters respond. But for precise settings and a wider range of parameters, type settings into the edit fields. (For this reason, the connection between sliders and edit fields are one-way—sliders update the edit fields, but changing the fields does not change the sliders positions accordingly.)

Review the biquad direct forms here; direct form I is best for fixed point processors, while direct for II transposed is best for floating point implementations.

Posted in Biquads, Digital Audio, Filters, IIR Filters, Widgets | 35 Comments

Envelope generators—ADSR widget

Attack Curve
Decay/Release Curve

This is the widget I used in making the ADSR video. It’s a JavaScript recreation of my C++ source code.

Posted in Envelope Generators, Synthesizers, Widgets | 7 Comments

Envelope generators—ADSR video

Let me know how you like this one!

Posted in Envelope Generators, Synthesizers, Video | 3 Comments

Envelope generators—ADSR code

First, a brief example of how to use the ADSR code:

// create ADSR env
ADSR *env = new ADSR();

// initialize settings
env->setAttackRate(.1 * sampleRate);  // .1 second
env->setDecayRate(.3 * sampleRate);
env->setReleaseRate(5 * sampleRate);
// at some point, by MIDI perhaps, the envelope is gated "on"
// and some time later, it's gated "off"

In your “real-time” thread, where you fill audio buffers for output, you’d use the process command to generate and return the next ADSR output:

// env->process() to generate and return the ADSR output...
outBuf[idx] = filter->process(osc->getOutput()) * env->process();


Create and destroy:


Call the process function at the control rate (which might be once per sample period, or a lower rate if you’ve implemented a lower control sampling rate); it returns the current envelope output. The getOutput function returns the current output only, for convenience:

float process(void);
float getOutput(void);

Set the gate state on (true) or off (false):

void gate(int on);

Set the Attack, Decay, and Release rates (in samples—you can multiply time in seconds by the sample rate), and the sustain level (0.0-1.0); calls these when settings change, not at the sample rate:

void setAttackRate(float rate);
void setDecayRate(float rate);
void setReleaseRate(float rate);
void setSustainLevel(float level);

Adjust the curves of the Attack, or Decay and Release segments, from the initial default values (small number such as 0.0001 to 0.01 for mostly-exponential, large numbers like 100 for virtually linear):

void setTargetRatioA(float targetRatio);
void setTargetRatioDR(float targetRatio);

Reset the envelope generator:

void reset(void);

It may be useful to know what state an envelope generator is in, for sophisticated control applications (typically, though, you won’t need this); a state enum is defined for convenience (for example, ADSR::env_sustain is equivalent to the value 3, and indicates that the current state is Sustain):

int getState(void);
    env_idle = 0, env_attack, env_decay, env_sustain, env_release


Calculations that are done in the “real time” thread are written as inline code in the header file. Calculations that are done asynchronously, at “setup time” (which include patch recall and “knob twiddling”), are in the cpp file functions; this includes sub-calculations of the real-time math that are dependent only on setup-time parameters.

Download ADSR source code

Posted in Envelope Generators, Source Code, Synthesizers | 10 Comments