MATLAB: Frequency index to hertz

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I think I'm just finally starting to get the hang of the frequency spectra.. say I have a signal that has undergone a Fourier transform so it is now plotted as the frequency vs its index. I want to find the beats per minute of this signal. If the signal had a sampling frequency of 50 Hz and 100 data points, and the first peak of the signal was located at the 20th index, would that equate to 10 Hz? As I would have index*sampling_frequency/total_points? And since Hz is measured as beats per second, I would multiply that by 60 to have a total of 600 beats per second?

Best Answer

If the time-domain signal has a sampling frequency of 50 Hz and 100 data points, the one-sided frequency_domain plot will have a frequency vector going from 0 to 25 Hz with 51 points.

So in the frequency-domain plot, a peak at the 20th index would correspond to 25*20/51=9.8 Hz.

So 10 Hz is essentially correct. It is not exact because of the way the discrete Fourier transform is calculated and plotted. This is the sort of compromise that is inherent in all discrete signal processing.

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MATLAB: How do i normalise frequency axis after computing fft

If you have a 50 Hz sampling frequency, the Nyquist frequency — in this instance the normalising frequency if you are designing a digital filter — is 25 Hz. So if you want a 15 Hz cutoff for a lowpass filter for instance, the normalised frequency, ‘Wn’ would be:

Fs = 50;                    % Sampling Frequency (Hz)
Fn = Fs/2;                  % Nyquist Frequency (Hz)
Fc = 15;                    % Cutoff Frequency (Hz)
Wn = Fc/Fn;                 % Normalised Cutoff Frequency (Dimensionless)

So Wn = 15/25 = 0.6

EDIT — For fft scaling, the best documentation is in the R2015a fft version. See specifically the code between the first two plot images.

MATLAB: How to know the baseband (BB) from FFT

If you have the frequency-domain samples, you can use the ifft function to get the time-domain samples. Following this, use the biterr function with you time-domain samples and the original transmitted sequence to determine the Bit-Error Rate.

Hope this helps!

Best Answer

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MATLAB: How do i normalise frequency axis after computing fft

MATLAB: How to know the baseband (BB) from FFT

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