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Appendix F. Window Functions

Windowing functions are used for analysis, and as waveform envelopes, particularly in granular synthesis. Window functions are built in to some opcodes, but others require a function table to generate the window. GEN20 is used for this purpose. The diagram of each window below, is accompanied by the f score statement and ftgen orchestra opcode used to generate it.

Hamming

Example F.. Hamming window function statement
f81   0   8192   20   1   1

i0 ftgen 81, 0, 8192, 20, 1, 1
Hamming Window Function.
Hamming Window Function.

Hanning

Example F.2. Hanning window function statement
f82   0   8192   20   2   1

i0 ftgen 82, 0, 8192, 20, 2, 1
Hanning Window Function
Hanning Window Function

Bartlett

Example F.3. Bartlett window function statement
f83   0   8192   20   3   1

i0 ftgen 83, 0, 8192, 20, 3, 1
Bartlett Window Function
Bartlett Window Function

Blackman

Example F.4. Blackman window function statement
f84   0   8192   20   4   1

i0 ftgen 84, 0, 8192, 20, 4, 1
Blackman Window Function
Blackman Window Function

Blackman-Harris

Example F.5. Blackman-Harris window function statement
f85   0   8192   20   5   1

i0 ftgen 85, 0, 8192, 20, 5, 1
Blackman-Harris Window Function
Blackman-Harris Window Function

Gaussian

Example F.6. Gaussian window function statement
f86   0   8192   20   6   1

i0 ftgen 86, 0, 8192, 20, 6, 1
Blackman-Harris Window Function
Blackman-Harris Window Function
Example F.6a. Gaussian window function statement with extra parameter
f61 0 8192   20   6   1 2

i0 ftgen 61, 0, 8192, 20, 6, 1, 2
Gaussian Window Function
Gaussian Window Function

Kaiser

Example F.7. Kaiser window function statement as default (alpha=0)
f87  0   8192   20   7   1

i0 ftgen 87, 0, 8192, 20, 7, 1
Gaussian Window Function
Gaussian Window Function
Example F.7a. Kaiser window function statement with alpha=5
f71  0   8192   20  7   1  5

i0 ftgen 71, 0, 8192, 20, 7, 1, 5
Gaussian Window Function
Gaussian Window Function
Example F.7b. Kaiser window function statement with alpha=10
f72  0   8192   20   7   1  10

i0 ftgen 72, 0, 8192, 20, 7, 1, 10
Kaiser Window Function
Kaiser Window Function

Rectangle

Example F.8. Rectangle window function statement
f88   0   8192   -20   8   .3

i0 ftgen 88, 0, 8192, -20, 8, .3
Rectangle Window Function
Rectangle Window Function

Sinc

Example F.9. Sinc window function statement (default and max=0.8)
f89  0   8192   -20   9   .8

i0 ftgen 89, 0, 8192, -20, 9, .8
Rectangle Window Function
Rectangle Window Function
Example F.9a. Sinc window function statement (-3π to +3π and normalized)
f89  0   8192   20   9   1  3

i0 ftgen 89, 0, 8192, 20, 9, 1, 3
Sinc Window Function
Sinc Window Function