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.1. 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


Example F.7. 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.8. Kaiser window function statement as default (alpha=0)

f87  0   8192   20   7   1
i0 ftgen 87, 0, 8192, 20, 7, 1


Example F.9. Kaiser window function statement with alpha=5

f71  0   8192   20  7   1  5
i0 ftgen 71, 0, 8192, 20, 7, 1, 5


Example F.10. 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.11. 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.12. Sinc window function statement (default and max=0.8)

f89  0   8192   -20   9   .8
i0 ftgen 89, 0, 8192, -20, 9, .8


Example F.13. 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