To show:

or

From the DFT case [264], we know this is true when and are each complex sequences of length , in which case and are length . Thus,

(3.38) |

where we have chosen to keep frequency samples in terms of the original frequency axis prior to downsampling,

(3.39) |

Replacing by and converting to -transform notation instead of Fourier transform notation , with , yields the final result.

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University