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Signal for Windows version 3
Hilbert transformer
A Hilbert transformer phase shifts a band of frequencies from Flow to Fhigh by -π/2. The
target magnitude response in the band is to leave the magnitude unchanged. Flow must be
greater than 0 and for the minimum magnitude overshoot in the undefined regions, Fhigh
should be 0.5-Flow. The magnitude response at 0 is 0, and if an odd number of
coefficients is set, then the response at 0.5 is also 0. This means that if you want Fhigh to
be 0.5 (or near to it), you must use an even number of coefficients.
There is a special case of the transformer where there is an odd number of coefficients
and Fhigh = 0.5-Flow. In this case, every other coefficient is 0. This is no help to the MSF
and MSF programs, but users who write their own software can use this fact to minimise
the number of operations required to make a filter.
It is extremely unlikely that a Hilbert transformer will be of any practical use in the
context of Signal, so we do not consider them further. You can find more information
about this type of filter in Theory and Application of Digital Signal Processing by
Rabiner and Gold.
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