Designing high pass filters with remez from DSP

Specific Domains Signal and Image Processing
1

When using the remez function from DSP to design high pass filters, the result is not what I expect. Here is an MWE (1.12.7 plus latest DSP):

using DSP

h = remez(32, [(0.0, 0.2) => 0.0, (0.3, 0.5) => 1.0])
h_obj = PolynomialRatio(h,[1])
H, fax = freqresp(h_obj)
# Plotting here ..

This gives the following frequency response:

hp
hp1200×900 56.9 KB

On the other hand, changing the filter to lowpass with the exact same conditions gives us a proper filter:

using DSP

h = remez(32, [(0.0, 0.2) => 1.0, (0.3, 0.5) => 0.0])
h_obj = PolynomialRatio(h,[1])
H, fax = freqresp(h_obj)
# Plotting here

lp
lp1200×900 22.6 KB

What am I missing here?

2

So, it turns out that using an even filter order does not work for high pass filters, while odd ones do. Not sure if this is some theoretical limitation or a implementation mishap, but there it is. Should probably be mentioned somewhere anyways…

3

For highpass linear-phase FIR filters we need an odd number of taps because an even number forces a zero gain at Nyquist (not a problem for low-pass filters).