What if the frequencies are equally spaced between
Then
Given a desired frequency response, the frequency sampling
design method designs a filter with a frequency response
exactly equal to the desired response at a
particular set of frequencies
What is
or
What if the frequencies are equally spaced between
Then
Removing linear phase from both sides yields
To yield real coefficients,
Simlar equations exist for even lengths, anti-symmetric, and
This method is simple conceptually and very efficient for
equally spaced samples, since
Possible solution to this problem: specify more frequency samples than degrees of freedom, and minimize the total error in the frequency response at all of these samples.
For the samples
For
Here we will consider the
To minimize the
The minimum error norm solution is well known to be