MATLAB: Result of FFT command is not good

bandwidthdftfftfrequency responsesystam identification

Hello every body. I used fft command for recognize bandwidth of a set of datas… First data pack has nearly 25000 time domain data with 25 seconds sampling time and next data pack has 12000 time domain data with 1 second sampling time, then result of fft and its absolute value are same, we know from nyquist sampling theory that by 25 seconds sampling time we cant have freqeuncy above o.o2 Hz and by 1 second sampling time we cant have freqeuncy above 0.5 Hz, but result are same similar attached picture… Red graph is 1 seconds sampling time and blue graph is 25 seconds sampling time, please care that horizontally must be multiply "0.01" and its dimension is rad/s and vertically is amplitude of signal… Please help me. Thanks alot.

Best Answer

Remember that the duration of the data pack will affect frequency domain sampling according to

    deltaFrequency=1/time_duration

So, your first data pack is getting its spectrum sampled at increments of .04 Hz while your second pack is being sampled at 1 Hz increments. Also keep in mind that this is not a continuous Fourier transform. To scale the FFT consistently with the continuous Fourier transform, you must multiply by the time sampling interval, which is also different for each of your two data packs.

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MATLAB: Frequency index to hertz

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.

MATLAB: Is 0.001Hz resolution possible with a 2.5Ms/s file while preserving the time resolution

It sounds like you have

    dt = 1/2.5e6;
    N = 600/dt;

N samples is that correct? To achieve a frequency resolution of 0.001 Hz with a sampling rate of 2.5 megahertz you need

   1/(0.001*dt)

samples, which you don't have. Padding the fft does not increase your frequency resolution. That is determined by your sampling rate and the number of samples you acquire. Padding the fft() only interpolates the frequency grid.

So in short, no, you don't have enough data for the DFT to have 0.001 Hz resolution, let alone the short-time Fourier transform for which you would have to segment your data.

Best Answer

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MATLAB: Frequency index to hertz

MATLAB: Is 0.001Hz resolution possible with a 2.5Ms/s file while preserving the time resolution

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