Selective Fourier transform (ZOOM-FFT)

The principle of selective Fourier transform you can read a book. The approximate steps are

1. Frequency shift (moves the center frequency of the selection to zero frequency)
   
2. Digital low-pass filter (prevents frequency aliasing)
   
3. Resampling (sampling data is sampled again, interval data depends on the bandwidth of the analysis, which is the magnification)
   
4. Complex FFT (the data is not a real number since it has been shifted frequency)
   
5. Frequency adjustment (Shift the frequency component of the negative half axis to the positive half axis)

The procedure is as follows:

function [f, y] = Zfft (x, FI, FA, FS)% x for the collected data% fi for the analysis of the starting frequency% FA for the analysis of the cutoff frequency% FS for the sampling frequency of the acquisition data% F for the output frequency sequence% y for the output amplitude sequence (real number) F0 = (fi + F a)/2;              % Center Frequency n = length (x);                 % data Length r = 0:n-1;b = 2*pi*f0.*r./fs;               X1 = x. * EXP ( -1j. * b);          % frequency shift bw = FA-FI;                                                             B = Fir1 (+, bw/fs);             % filter cutoff frequency is 0.5bwx2 = Filter (B, 1, x1);               c = X2 (1:floor (FS/BW): N);           % resampling N1 = Length (c), F = linspace (FI, FA, N1), y = ABS (FFT (c))./N1 * 2;                         y = Circshift (y, [0, Floor (N1/2)]);            % moves the amplitude of the negative half axis over the end

Application Examples:

FS = 2048; T = 100;t = 0:1/fs:t;x = * COS (2*pi*110.*t) + (2*pi*111.45.*t) + 25*cos (2*pi*112.3*t) + 48*cos (2*pi*113.8.*t) +5 0*cos (2*pi*114.5.*t); [F, Y] = Zfft (x, 109, $, FS);p lot (f, y);

Effect:

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Selective Fourier transform (ZOOM-FFT)