Pre-Class Music

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Pre-Class Music

• Roger Reynolds, Transfigured Wind IIBSU
  catalog no. CD 3204

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Convolution

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Convolution Background

• Fundamental operation in digital audio
  processing.
• Even if you dont 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.

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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.

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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.
• length(output) length(a) length(b) - 1

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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.

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The Law of Convolution

• Convolution in the time domain is equal to
  multiplication in the frequency domain, and vice
  versa.
• (btw, thats an important conceptit will be on
  the test.)
• convolution does not distinguish between samples
  and spectra. Both are series of discrete values.

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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.

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Musical Uses of Convolution

• Filtering frequencies present in both signals
  are reinforced frequencies only present in one
  signal will be eliminated.
• Reverberation convolution has time domain
  results, including echo and time smearing, which
  can be used to recreate reverb.