## Outline

• Convolution
• Reverb
• Reverb (lab)
• Audio File Formats
• Wavetable ann Additive Synthesis (lab)

source: https://ccrma.stanford.edu/software/clm/compmus/clm-tutorials/processing2.html#rev

## Reverb

##### Convolution 1
An impulse function: delta(n)={(1, n=0), (0, otherwise):}
x(n)=sum_(k=-oo)^oox(k)delta(n-k)

A system (a transform): y(n)=T[x(n)]

y(n)=T[sum_(k=-oo)^oox(k)delta(n-k)]

If T is linear:
(i.e., T[alpha f(n)+beta g(n)] = alpha T[f(n)]+beta T[g(n)])
y(n)=sum_(k=-oo)^oox(k)T[delta(n-k)]
##### Convolution 2
Assuming T is linear:
y(n)=sum_(k=-oo)^oox(k)T[delta(n-k)]
If T is also time invariant:
y(n) = T[x(n)] -> y(n-k) = T[x(n-k)]
If h(n) is a response of T to delta(n) then:
h(n) = T[delta(n)] -> h(n-k) = T[delta(n-k)]
y(n)=sum_(k=-oo)^oox(k)h(n-k)
But h(n) is the impulse reponse of T
##### Convolution 3
This is the definition of convolution:
y(n)=sum_(k=-oo)^oox(k)h(n-k)
Also noted as: y(n) = x(n) * h(n)

##### Fast Convolution
y(n) = IFT{FT[x(n)] * FT[h(n)]}
The convolution is the same as the inverse Fourier transoform of the multiplication of the input and the impulse response in the frequency domain!

## Audio File Format

• List of different audio file formats
• Compressed vs Uncompressed
• Why compress?
• How much can it be compressed?
• Lossless vs Lossy
• When do you not want to compress, even lossless?
• Sound quality
• Open vs Proprietry technologies
• Containers
• DRM

## Uncompressed (lossless) audio file format

• Bit width: 16-24 bits
• Sampling rates: 44.1kHz, 48kHz, 96kHz, 192kHz
• PCM (header less): Pulse-coded Modulation
• AIFF (Audio Interchange File Format)
• WAVE & WAVE BWF

## Compressed audio file format

• Lossless (typically 2:1)
• FLAC (Free Lossless Audio Codec)
• WMA Lossless
• Lossy (up to 10:1 or more)
• MP3: MPEG I/II Layer 3
• Ogg Vorbis
• WMA
• AAC

## Lossy Perceptual Audio Coding

• MP3 (MPEG I/II Layer III)
• Karlheinz Brandenburg
• Stereo or 5.1 channels
• Sampling frequency: 16-48kHz
• AAC (Advanced Audio Coding; 1997)
• m4a: created by iTUnes when importing from CDs
• m4p (DRM protected): when you buy a song from Apple on iTunes (as of 2009/01, iTunes offer DRM-free songs)
• Up to 48 channels
• Sampling frequency: 8–96kHz

## Containers

• Audio only
• AIFF (Apple 1989)
• WAV (Microsoft & IBM 1991)
• General (multimedia)
• Matroska
• Ogg
• MPEG: MP4
• AVI
• AES-31
• METS

## IFF File Format

• Interchange File Format: AIFF (big-endian), RIFF (little-endian), WAV (not TIFF)
• Based on "EA IFF 85"
• Based on "chunks"
• Extensible

## Lossy vs Lossless

• Q: Can people hear the difference?
• A: It depends
• Listeners can tell the difference between CD quality and MP3 compression (92–192 kb/s) [Amandine et al. 2009]
• Listeners can not tell the difference between CD quality and MP3 compression (256–320 kb/s) [Amandine et al. 2009]
• Listening test

### MUMT 307

• Using the PeriodicWave demo, create a sawtooth wavetable and a triangular wavetable with the following Fourier series with the fundamental frequency f (lab):
• Square: 4/pisum_(k=0)^oo 1/k sin(2pifkt) text{ for } k=1,3,5,...
Sawtooth: 1/2 - 1/pisum_(k=0)^oo 1/k sin(2pifkt) text{ for } k=1,2,3,...
Square: 8/pi^2sum_(k=0)^oo (-1)^{(k-1)//2}/k^2 sin(2pifkt) text{ for } k=1,3,5,...