Design lowpass kaiser filter for hourly tides

Hi all,

I am trying to design a low-pass Kaiser filter for some hourly tide data so that I can apply filtfilt before harmonically analyzing the dataset. I attempted to modify the filter for http://www.mathworks.com/matlabcentral/answers/260004-design-of-a-highpass-filter-with-a-kaiser-window. I need my cutoff frequency be greater than 12 cycles per day. Here's what I did:

Ts = 1/24;                           % Sampling Interval (Day) 3 Hours = 3/24 Days
Fs = 1/Ts;                           % Sampling Frequency (1/Day)
Fn = Fs/2;                           % Nyquist Frequency (1/Day)
Fc = 24/11;                           % Cutoff Frequency (1/Day)
Fp = 24/12;                          % Passband Frequency (1/Day)
band_edges = [Fp Fc]/Fn;             % Normalised Band Edges
mag_vct = [1  0];                    % Specify Highpass
sb_att = 0.045;                      % Stopband Attenuation (dB)
pb_rpl = 0.01;                       % Passband Ripple (dB)
devs = [pb_rpl sb_att];              % Filter Specifications Vector

[n,Wn,beta,ftype] = kaiserord(band_edges,mag_vct,devs,Fs);              % Design Filter
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');                       % Create Filter

fzv = linspace(0, 1, 1000)*Fn;                                          % Frequency Vector
freqz(hh, 1024, fzv, Fs)

I also tried:

d = designfilt('lowpassfir','PassbandFrequency',Fp,...
'StopbandFrequency',Fc,'PassbandRipple',pb_rpl,...
'StopbandAttenuation',sb_att,'SampleRate',Fs, ...
'DesignMethod', 'kaiserwin');

hfvt = fvtool(d);

However, neither of these give the desired result and they are not the same.

Answer 1

[Star Strider]

I’m not certain what you want your filter to do. If your sampling interval, ‘Ts’ is 1/24 day, your sampling frequency is 24 cycles/day, and your Nyquist frequency (the highest resolvable frequency in a sampled signal) is 12 cycles/day. (The Nyquist frequency is the hard upper limit to any discrete filter.) So if you want a filter to pass everything below 12 cycles/day, you’re essentially not filtering it — you’re passing all the frequencies your instrumentation can resolve.

Do you want your filter to have a 2 cycles/day cutoff? (That would make sense for tides, but I would design it to have a cutoff of 3 or 4 cycles/day to be certain to capture all the information necessary to define a tidal signal.)

Note that oceanography is not an area of my expertise. I may be missing something.