designing a chebyshev type 2 high pass filter

Hello

I am trying to design a chebyshev type 2 filter to separate the body acceleration and gravity acceleration from my senor. This is what I am basing the design from with a stopband attenuation of 60 dB and stopband frequency of 0.4 Hz. My sensor (ICM20948) is sending out acceleration data at a rate around 56 HZ. This is what I have so far.

Fs=56% from my sensor
[b,a,c] = cheby2(9,0.04,60/1000,'high');
sos = zp2sos(b,a,c)
fvtool(sos)

Any help would be much appreciated

Answer 1

[Star Strider]

Start with the cheb2ord function to define all the variables appropriately.

[kelvin]

Whats the diffrence between cheb2ord() vs cheby2?

[Star Strider]

The cheb2ord function creates the necessary variables that cheby2 uses.

Please see the documentation for an extended description of the two functions.

[kelvin]

Thank you. I understand it now.

[Star Strider]

As always, my pleasure!

On the basis of the Fourier transform, I designed a different sort of filter, and used a muich more efficient elliptical design. I also resampled it to a constant sampling frequency of 10 Hz.

See if this does what you want:

Da = load('acceleration.mat');
Dt = load('time.mat');

acceleration = Da.accleration;
t = Dt.time;

Ts1 = mean(diff(t));
Fs1 = 1/Ts1;

Fsr = ceil(Fs1/10)*10;                                              % Sampling Frequency For Resampled Data
[accr,tr] = resample(acceleration, t, Fsr);                         % Resample Data To Constant Sampling Frequency

Fn = Fsr/2;                                                         % Nyquist Frequency
L = numel(tr);
accrc = accr - mean(accr);                                          % Subtract Mean (Makes Other Peaks More Prominent)
FTaccr = fft(accrc)/L;                                              % Normalised Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                                 % Frequency Vector
Iv = 1:numel(Fv);                                                   % Index Vector (One-Sided Fourier Transform)

figure
plot(Fv, abs(FTaccr(Iv,:))*2)
grid
title('Fourier Transform')
xlabel('Frequency (Hz)')
ylabel('Amplitude')

Wp = [0.01 0.75]/Fn;                                                % Stopband Frequency (Normalised)
Ws = [0.99 1.01].*Wp;                                               % Passband Frequency (Normalised)
Rp =  1;                                                            % Passband Ripple
Rs = 60;                                                            % Passband Ripple (Attenuation)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                                     % Elliptic Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp);                                        % Elliptic Filter Design: Zero-Pole-Gain 
[sos,g] = zp2sos(z,p,k);                                            % Second-Order Section For Stability

figure
freqz(sos, 2^20, Fsr)                                                % Filter Bode Plot
set(subplot(2,1,1), 'XLim',Wp*Fn.*[0.8 1.2])                        % Optional
set(subplot(2,1,2), 'XLim',Wp*Fn.*[0.8 1.2])                        % Optional

accr_filtered = filtfilt(sos, g, accr);                             % Filter With IIR Filter

sbp = size(accr,2);
figure
for k = 1:size(accr,2)
    subplot(sbp,1,k)
    plot(tr, accr(:,k))
    hold on
    plot(tr, accr_filtered(:,k))
    hold off
    grid
    title(sprintf('Column %d', k))
    xlabel('Time (s)')
    ylabel('Amplitude')
    legend('Original','Filtered')
end

This uses a nuch more efficient elliptical filter design and implementation than a Chebyshev (or essentially any other) filter. It is a bandpass filter, so it eliminates the d-c (constant) offset, as well as high-frequency noise. I set the upper cutoff frequency at 0.75 Hz, so experiment with that if you want more (higher frequency) or less (lower frequency) detail in the signal.

.

[kelvin]

Thank you once again. I'll defintly look into elliptical filters.

[Star Strider]

As always, my pleasure!

Answer 2

[Bilawal]

Fs=56% from my sensor

[b,a,c] = cheby2(9,0.04,60/1000,'high');

sos = zp2sos(b,a,c)

fvtool(sos)