1. Pre-Class Music Keith Kothman, Interludes video by John Fillwalk

2. Convolution

3. Convolution Background Fundamental operation in digital audio processing. Even if you don’t specifically know it, you know its effects (through filtering, modulation, reverberation, cross synthesis).  A filter convolves its IR with the input signal to produce filtered output.

4. Uses of Convolution Reverberation  obtain the IR of a room, and convolve it with an arbitrary signal to make it sound as if the arbitrary signal has been played in that room. Filtering  arbitrary signals  to model the characteristics of an audio system, such as a microphone or guitar amp.

5. The Math of Convolution The equation (the * denotes convolution)  for every sample in the arbitrary signal a, multiply it by every sample in the IR b, and sum the results (offset by each sample in a)  length(output) = length(a) + length(b) - 1 in samples

6. Convolution is not Multiplication Multiplication of two audio signals is amplitude modulation  for each point in time, one sample is multiplied by another sample. Convolution of two audio signals is a series of multiplications, and a summation of those results.  every sample in one signal is multiplied by the entire set of samples in the second signal.

7. The Law of Convolution Convolution in the time domain is equal to multiplication in the frequency domain, and vice versa.  (btw, that’s an important concept—it will be on the test.)  convolution does not distinguish between samples and spectra. Both are series of discrete values.

8. Implementation of Convolution Direct Convolution of amplitude samples is computationally intensive. Fast Convolution is preferred.  an FFT is performed on each audio signal, and their corresponding spectra are multiplied.  an inverse FFT is applied to the result.

9. Musical Uses of Convolution Filtering: frequencies present with high amplitude levels in both signals are reinforced; frequencies only present in one signal are eliminated. Reverberation: convolution has time domain results, including echo and time smearing, which can be used to recreate natural or artificial reverb, or to otherwise distort and blur the original source material.