Calculate group delay out of phase response - Usage of FIR differentiator ?

I would like to show a bode plot and the corresponding group delay for some filter application.

I've got a simulink model of my filter. I use band-limited white noise as the input signal and record the output signal of my filter.

To create an simple example I am just using the transfer function of my filter to show the principle problem.

% Create binomial filter of order N=100

N=100;z = tf('z', Thf)

filte_HF=(2^(-N)*(1-z^(-1))^(N));

% Show bode plot in Hz

options=bodeoptions;

options.FreqUnits = 'Hz';

% Create frequenc vector

delta_f = 1e-1;

f = 1:delta_f:2000;

w=2*pi*f;

% Calculate bode diagram

[mag,phase,w]=bode(filte_HF, options,w);

phi=squeeze(phase);

% Plot Bode diagram

figure(1);

bode(filte_HF,options);grid on;hold on;

% Calculate group delay using Matlab function

[gd,wgrp]=grpdelay(cell2mat(filte_HF.Numerator),cell2mat(filte_HF.Denominator),f,1/Thf);

% Compare group delay of Matlab function and manually calcuated group delay

% out of the phase response

figure(2);

semilogx(f,gd*Thf);hold on;

semilogx(f(1:end-1),-diff(deg2rad(phi))./diff(w),'--');

% semilogx(f,filter(Hd,-deg2rad(phi)));

ylim([0 50e-3]);

Questions:

1) Why is the result of the matlab function grpdelay different from the manually calculated groupdelay with -diff(deg2rad(phi))./diff(w)?

2) I want to use the original noisy signals from my simulink model. I use tfestimate to get the transfer function estimate and then angle(txy). I get a phase reponse which is also a little more noisy. Out of this I also want to calculate the group delay that means the derivative of the phase reponse. To cope with that problem I found that a differentiator filter could be used. Example:

https://de.mathworks.com/help/signal/ug/take-derivatives-of-a-signal.html

My problem is how to design the filter if I don't want to differentiate a time-based signal, but a frequency-based signal, which is the phase response? How to chose the passband and stopband frequency and sample frequency?

Nf = 50;

Fpass = ??;

Fstop = ??;

Fs=??

Hd = designfilt('differentiatorfir','FilterOrder',Nf, ...

'PassbandFrequency',Fpass,'StopbandFrequency',Fstop, ...

'SampleRate',Fs);

3) Are there other options to solve that problem?

[Devyani Varshney]

Hi did you find any solution. I am also looking for the same.

[Paul]

Solution to which of the three questions?

[Devyani Varshney]

for all of the above three questions.