Teaching

Resources relating to my teaching are collected here. See also the Resources page for some related tools and demos.

Musical Applications of Fourier Theory and DSP (course link)

Lecture 1: Signals, Sinusoids, and Complex Exponentials

Building a sound out of sinusoids	Shows that by adding together just the right amplitude and phase of a set of sinusoids, a complex audio signal can be synthesised. Any mono audio signal is exactly the sum of sinusoids at its DFT frequencies. Add them in from the lowest frequency upward, and listen to the sound assemble itself.
Quantisation and bit depth in digital audio	Explore the effect of level quantisation, controlled via bit-depth, on the sound of digital audio files.
Taylor series reconstruction	Interactive demo showing Taylor series reconstruction of a few common functions.
Cosine and sine functions as projections from a rotating phasor	Interactive animation illustrating the generation of cosine and sine functions from a rotating phasor.
Beating and psychoacoustic roughness	What happens if we add together a pair of periodic signals where the frequencies are similar, but not quite the same? If the signals are simple sinusoids, we get interesting “beating” effects. If the signals are each rich in harmonics, such as sawtooth waves, human listeners experience quite particular psychoacoustic effects – sometimes called “roughness”.
Damped sinusoids and complex frequency	Interactive demo showing the generation of a damped sinusoid via the idea of complex frequency.

Lecture 2: Continuous-time Spectral Representations

Two phasors make a single real sinusoid	Interactive demo showing how a pair of oppositely rotating phasors (one of positive frequency, one of negative frequency) combine to make a single real sinusoid.
The spectrum as a recipe	Interactive demo showing how a combination of just a handful of sinusoids can produce a time waveform that is complicated, and potentially even not periodic.
Using Fourier series to build audio waveforms	Interactive demo showing an audio waveform is created by combining 1 or more harmonic frequency components.

Lecture 3: Discrete-time and Basic Filters

Sampling a complex phasor	Interactive demo showing how sampling a complex phasor at discrete time intervals creates a discrete-time signal. Concepts such as aliasing and bandwidth are included.
The wagon wheel and aliasing	Interactive demo showing the classic demonstration of aliasing and folding.
Digital synthesis of square and sawtooth waveforms	Synthesising a square wave, or sawtooth wave, will give very different results, depending on how the wave is put together. A partial Fourier series sum, via the frequency domain, is a much better way that naively making a “square” waveform in the time domain.

Lecture 4: LTI Systems in Discrete Time

Numerical measurement of FIR frequency response	Impulse responses of various basic feedforward (FIR) filters are applied to different inputs, and the resulting output plotted point-by-point. Taking the magnitude of the result provides a numerical estimate of the frequency response at the given frequency.
Discrete convolution step-by-step	The output of an LTI filter can be obtained by convolving an input with the filter’s impulse response . This discrete convolution operation can be understood as “flipping” and running it over , computing the sum of point-wise products of the overlapping samples at each time step.