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.

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

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

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-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

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

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

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

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