Victoria - 2021-03-18T11:29:04+00:00
Question: Why does the CHEBWIN function give incorrect results in Signal Processing Toolbox 6.1(R13SP1)?
When I use the following code: wvtool(chebwin(4096,30)) The main lobe of the time response does not have a peak at 1.0 as expected. However, if I use the code: wvtool(chebwin(4096,60)) I receive a peak amplitude of 1.0. I should receive a peak amplitude of 1.0 in all situations.
Expert Answer
John Williams answered .
2025-11-20
This enhancement has been incorporated in Release 14 Service Pack 3 (R14SP3). For previous product releases, read below for any possible workarounds:
An artifact of the equiripple design method used in the CHEBWIN function is the presence of impulses at the endpoints of the time-domain response. This is due to the constant-level sidelobes in the frequency domain. The magnitude of the impulses are on the order of the size of the spectral sidelobes. If the sidelobes are large, the effect at the endpoints may be significant.
For these cases, the time domain Chebyshev window actually has higher magnitude impulses at the end-points than the middle window tap. Also, since we normalize the window weights, all the remaining window weights are less than 1. This is expected behavior and is an artifact of the equiripple design of the Dolph Chebyshev window.
The same phenomenon exists for any equirripple FIR filter, that is, any filter that has constant level side-lobes in its frequency domain has impulses in its time series. These impulses are always present for an equiripple design but their size is on the order of the size of the spectral side-lobes and may be overlooked on the scale of the filter coefficient set.
For more information on that topic, see section 3.3.1, 'Equiripple vs. 1/f Ripple Designs in 'Multirate Signal Processing for Communication Systems' by Fredric J. Harris, Prentice Hall PTR.
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