CODEWITHSUNDEEP
matlabsignal-processingfft
code-gijoe
code-gijoe

Reputation: 7234

How to compute the CTFT using matlab?

I'm trying to find a factor using matlab that requires me to compute the Fourier transform of an input signal. The problem was stated to me this way:

fbin = 50HZ
0 <= n <= 1999
alpha = F {Blackman[2000] . cos[-2pi . fbin . n/2000]} (f)

where F is the Continous Time Fourier Transform operator.

My matlab code looks like this:

blackman_v = blackman(2000);
signal_x = cos(-2 * pi() .* fbin * (0:(1999)) ./ 2000) .* blackman_v';
fft_real = abs(fft(signal_x, 2000));
alpha = fft_real(51); %51 is the bin for 50hz => or {(f * N/Fs)+1}==51

My problem is that I'm supposed to get a value of around 412 for 49hz but I get about 250 (I'm actually verifying some previous results). Did I wrongly translate the problem? I've been battling for quite a while and I really don't see anything wrong here. Thought the value a 50Hz (430) is ok.

Would really appreciate any hint!

EDIT

blackman_v = blackman(2000);
signal_x = cos(-2 * pi() .* fbin * (0:(1999)) ./ 2000) .* blackman_v';
alpha = abs(freqz(signal_x , 1, 2*pi*50/10000))

Do you know what the freqz is? I read matlab doc and it is still not to clear in my head.

Upvotes: 0

Views: 5197

Answers (1)

Fredrik
Fredrik

Reputation: 2317

Maybe I misinterpreted your question but Matlab is not for continuous time analysis. It's for numerical analysis only, with discrete values. You can however calculate the discrete time fourier transform (DFT) of your signal, the resolution of which will depend on the length of your signal. Are you using a Blackmann window because your signal is non-periodic?

How to calculate the FFT (DFT) in Matlab: http://www.mathworks.se/help/matlab/ref/fft.html

Any discrete Fourier transform will assume that your signal is periodic. If it isn't you will obtain spectral leakage where certain frequency peaks "leak" their energy to the sides resulting in less defined peak with smeared out frequency values. Thus, the time-domain signal is preferably made periodic before calculting the DFT - periodic to the extent that a general pattern is repeated, values does not have to exact between periods since noise can/will be inherent in the signal. Applying a window function to the time-domain signal before calculating the DFT will make the signal periodic but you will have change amplitude values and introduced a low frequency component.

Upvotes: 1

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