Matlab filter questions

MATLABsignal processing

I have an array of data, it is in time domain. Each data stands for the magnitude, and that data is sampled in a frequency of 10,000Hz.
I want to do a band pass filter between two frequencies f1, and f2. I think I need to do a low pass filter and a high pass filter. The signal does an FFT then goes through the two filters then do an inverse FFT.
My questions: is there an easy way to do the low pass and high pass filter? I don't know how to derive the transfer function based on the two cut off frequencies.

Does anyone know how?

Thanks

Best Answer

Building on Tristan's answer, here is some Octave Code which might or might not be Matlab compatible. The butter function derives the transfer function coefficients for you. alt text .

hz = 8000;
x = [1:1:hz*10];
t = x./hz;
pi = 3.1415;

% Create signal with 10 hz, 200 hz and 500 hz components
raw_signal = sin(10*2*pi*t)+sin(200*2*pi*t)+sin(500*2*pi*t);

% View Raw Signal Over .1 Second Window
plot(t, raw_signal)
title('Raw Signal with 10Hz, 200Hz, 500Hz Components')
xlabel('Time (Sec)')
ylabel('Amplitude')
set(gca,'XLim', [5, 5.1]);

% Create Band Pass Butterworth Filter
[S_numer, S_denom] = butter(5, [100/hz 350/hz]);
band_passed_signal = filter(S_numer, S_denom, raw_signal);

% View Band Pass Filtered Signal Over .1 Second Window
plot(t, band_passed_signal)
title('Band Pass Filtered Signal')
xlabel('Time (Sec)')
ylabel('Amplitude')
set(gca,'XLim', [5, 5.1]);

Related Solutions

Matlab – Lowpass/Bandpass filter design in MATLAB

I found this question which has so many views and still no good answer.

The following code will do what you need. Since no filter-type is specified, I used a butterworth-filter to demonstrate it. s is the input signal and x is the filtered signal. fs is the sampling rate in Hz.

% Design and apply the lowpass filter
order = 4;
fcut  = 8000;
[b,a] = butter(order,fcut/(fs/2),'low');
x     = filter(b,a,s);


% Design and apply the bandpass filter
order    = 10;
fcutlow  = 1000;
fcuthigh = 2000;
[b,a]    = butter(order,[fcutlow,fcuthigh]/(fs/2), 'bandpass');
x        = filter(b,a,s);

Matlab – Understanding Matlab FFT example

1) Why does the x-axis (frequency) end at 500? How do I know that there aren't more frequencies or are they just ignored?

It ends at 500Hz because that is the Nyquist frequency of the signal when sampled at 1000Hz. Look at this line in the Mathworks example:

f = Fs/2*linspace(0,1,NFFT/2+1);

The frequency axis of the second plot goes from 0 to Fs/2, or half the sampling frequency. The Nyquist frequency is always half the sampling frequency, because above that, aliasing occurs: Aliasing illustration

The signal would "fold" back on itself, and appear to be some frequency at or below 500Hz.

2) How do I know the frequencies are between 0 and 500? Shouldn't the FFT tell me, in which limits the frequencies are?

Due to "folding" described above (the Nyquist frequency is also commonly known as the "folding frequency"), it is physically impossible for frequencies above 500Hz to appear in the FFT; higher frequencies will "fold" back and appear as lower frequencies.

Does the FFT only return the amplitude value without the frequency?

Yes, the MATLAB FFT function only returns one vector of amplitudes. However, they map to the frequency points you pass to it.

Let me know what needs clarification so I can help you further.

Best Answer

Related Solutions

Matlab – Lowpass/Bandpass filter design in MATLAB

Matlab – Understanding Matlab FFT example

Related Topic