how to design IIR highpass filter with cutoff frequency of 20Hz and FIR bandpass filter with cutoff frequency of 10Hz and 15Hz?

Fs = 8000;                                              
Fn = Fs/2;
Wp = 20/Fn;
Ws =  3/Fn;
Rp = 0.2;
Rs = 40;
[n,Wn] = buttord(Wp,Ws,Rp,Rs);
[b,a] = butter(n,Wn,'high');
[sos,g] = tf2sos(b,a);
figure(1)
freqz(sos, 2048, Fs)

Answer 1

[Star Strider]

I can’t design a fir filter to those specifications with any of the fir design functions, regardless of the order of the filter. The normalised frequencies are simply too low and the passband too narrow.

The best I can do is a Chebyshev Type II filter:

Fs  = 8000;
Fn = Fs/2;
Wp = [10  15]/Fn;
Ws = [ 6  25]/Fn;
Rp = 10;
Rs = 40;
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);
[b,a] = cheby2(n,Rs,Ws);
[sos,g] = tf2sos(b,a);

figure(2)
freqz(sos, 2^16, Fs)
set(subplot(2,1,1), 'Xlim', [0 25])
set(subplot(2,1,2), 'Xlim', [0 25])

I also had to increase the fft length 2^16 and narrow the frequency axis to [0 25] to see the details of the passband. Note that a Chebyshev Type II filter has a flat passband, so you can state the passband ripple, ‘Rp’, to be essentially anything you want.

If you want a fir bandpass filter with those characteristics, you would probably have to design separate highpass and lowpass filters and cascade them. The best way to do this would be with dfilt objects, using dfilt.cascade.

[Issac Pang]

What is the simulink of this question?

[Star Strider]

I have Simulink but have not used it in many years. I cannot answer that.

[Issac Pang]

thank you very much,what is the cutoff frequency of the design filter?

[Star Strider]

Here, they are the passband frequencies:

Wp = [10  15]/Fn;

[Issac Pang]

how I get the final cutoff frequency? I need to combine this 2 filter and get it?

[Issac Pang]

Design filter using IIR highpass filter with cutoff frequency, fc1 = 20 Hz and FIR bandpass filter with cutoff frequency fc2 = 10 Hz and fc3 = 15 Hz. What is your designed filter and it cutoff frequency? This is the question given.

[Star Strider]

Use the fir1 function to design the bandpass filter (it is easy, but you will have to experiment with it), and use a variation of my code but with:

Wp = 20/Fn;
Ws = 18/Fn;

for the high-pass filter. See the documentation for the respective functions for information on how to use them. You will have to designate 'high' in the cheby2 call.

Note that you will probably have to specify a high-order fft length in your freqz call (consider 2^15) to see all the details of your filter Bode plot.

[Issac Pang]

I don't get it,what u mean is i need to change my IIR filter from Wp = 20/Fn; Ws = 3/Fn; to Wp = 20/Fn; Ws = 18/Fn;

and the FIR filter just follow the answer you given?

[Star Strider]

I don’t know where you’re going with this, but here are your filters:

Fs = 8E3;
Fn = Fs/2;
mv = [0  0  1  1  0   0];
fv = [0  9 10 15  16 Fn]/Fn;
hbp = fir2(2^15, fv, mv);

figure(1)
freqz(hbp, 1, 2^18, Fs)
set(subplot(2,1,1), 'XLim', [0  50])
title('Star Strider’s FIR Bandpass Filter')
set(subplot(2,1,2), 'XLim', [0  50])

Fs  = 8E3;
Fn = Fs/2;
Wp = 20/Fn;
Ws = 16/Fn;
Rp = 10;
Rs = 40;
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);
[b,a] = cheby2(n,Rs,Ws,'high');
[sos,g] = tf2sos(b,a);

figure(2)
freqz(sos, 2^16, Fs)
set(subplot(2,1,1), 'Xlim', [0 50])
title('Star Strider’s IIR Highpass Filter')
set(subplot(2,1,2), 'Xlim', [0 50])

<<www-mathworks-com-matlabcentral-answers-uploaded_files-53201-how-20to-20design-20IIR-20highpass-20filter-20with-20cutoff-20frequency-20of-2020Hz-20and-20FIR-20bandpass-20filter-20with-20cutoff-20frequency-20of-2010Hz-20and-2015Hz-20-231-20--202016-2005-2027.png>>

<<www-mathworks-com-matlabcentral-answers-uploaded_files-53203-how-20to-20design-20IIR-20highpass-20filter-20with-20cutoff-20frequency-20of-2020Hz-20and-20FIR-20bandpass-20filter-20with-20cutoff-20frequency-20of-2010Hz-20and-2015Hz-20-232-20--202016-2005-2027.png>>

They work. Have fun with them!

[Issac Pang]

so what is the cutoff frequency of the filter you shown?

[Star Strider]

This is apparently a homework problem (that I didn’t know at the outset), so you have to do the rest of this on your own. I don’t know what your professor wants you to do.

There are three cutoff frequencies that I can see, 10 Hz, 15 Hz, and 20 Hz. You probably have to cascade them to put them into one filter. There are several ways to do this using Signal Processing Toolbox functions, and other less efficient techniques not implemented in the Signal Processing Toolbox.

[Issac Pang]

Yes the question want me to combine all filter into one,can u show me how to do this by using Signal Processing Toolbox?

[Star Strider]

I would create dfilt objects from your filters, then use the dfilt.cascade function. That is the easiest way, although you may have to rewrite some of your code. Then convert the cascaded filter object to second-order-section representation with one of the dfilt sos conversion functions. That will create a stable filter.

[Issac Pang]

so which part of code need to change?

[Star Strider]

Read through the documentation for the dfilt functions to determine that. Then just follow the examples in the documentation, experiment with your own band-pass and high-pass filters to get the result you want for each, and then cascade them to see the result.

That is how I learned to work with the dfilt functions. The documentation explains it much better than I ever could.

[jolene kuan]

hi isaac pang, have you got the solution to this question?

[Issac Pang]

still figure it out