MATLAB: Ideal low-pass filter transfer function

fftfrequency domainlow passlowpassrectangular signalrectangularsignaltransfer function

i have a signal in frequency domain (that i made fft and fftshift before) and i need to multiply it by a transfer function of an ideal low-pass filter with bandwith around 25Hz. i can't use the lowpass function and i need to only use the simplest basic functions.

so since it is an ideal low-pass filter, i was thinking multiply my signal with a rectangular signal in frequency domain. but my question is i don't know how to write a rectangular signal transfer function in frequency domain. Any recommendations? Thank you.

Best Answer

The ‘ideal’ filter is symmetrical about the origin in the frequency domain (after doing the fftshift call), so will be 1 from -25 Hz to +25 Hz, and zero elsewhere. Define it as such, and then do the multiplication with the signal in the frequency domain. Then use ifftshift on the filtered signal, then ifft to return it to the time domain.

Be sure to scale the result correctly, since filtering removes much of the energy in the original signal.

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MATLAB: Low-pass filter

hsize=??          % define
h=fspecial('average',hsize);
filter_wmarked=imfilter(wmarked,h);

MATLAB: Low pass filter VS high pass filter

Calculate the Fourier transform of the filter from the signals.

t = ...;                                                    % Time Vector
s = ...;                                                    % Original Signal Vector
s_filtered = ...;                                           % Filtered Signal Vector
Ts = mean(diff(t));                                         % Sampling Interval (Assumes Constant Intervals)
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
L = numel(t);                                               % Signal Length
FTs = fft(s)/L                                              % Fourier Transform of Original Signal
FTs_filt = fft(s_filtered)/L;                               % Fourier Transform of Filtered Signal
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                         % Frequency Vector (One-Sided Fourier Transform)
Iv = 1:numel(Fv);                                           % Index Vector (One-Sided Fourier Transform)
H = FTs_filt ./ FTs;                                        % Complex Transfer Function
figure
subplot(2,1,1)
plot(Fv, abs(H(Iv)))
ylabel('Amplitude')
grid
subplot(2,1,2)
plot(Fv, angle(H(Iv)))
xlabel('Frequency')
ylabel('Phase')
grid
sgtitle('Bode Plot of Filter')

That should reveal the filter characteristics, as well as reasonably accurate aspects of its design (e.g. passband and stopband frequencies).

Best Answer

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MATLAB: Low-pass filter

MATLAB: Low pass filter VS high pass filter

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