Error in FFT calculation

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KALEESH
KALEESH 2023-10-3
评论： Star Strider 2023-10-3
Why the FFT value shows higher value in the cut signal when compared to whole signal, it should be opposite right?
close all
clear all
clc
load("allSignals.mat");
Fs = 50e6; % Sampling frequency
T = 1/Fs; % Sampling period
L = 7500; % change as required
t = (0:L-1)*T; % Time vector
X = allSignals(1,:);
plot(t,X)
title("Signal ")
xlabel("t ")
ylabel("X(t)")
% fft
Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f,P1)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")
figure ; % after cut
X1 = allSignals(1,500:1100);
L1 = length(X1);
Y1 = fft(X1);
P21 = abs(Y1/L1);
P11 = P21(1:L1/2+1);
P11(2:end-1) = 2*P11(2:end-1);
f1 = Fs*(0:(L1/2))/L1;
plot(f1,P11)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")

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采纳的回答

Star Strider
Star Strider 2023-10-3
Ran in:
The value for ‘L’ is 7500 and for ‘L1’ is 601.
If you change:
P21 = abs(Y1/L1);
to
P21 = abs(Y1/L);
you will get the expected result (magnitude of about 40 rather than about 500).
load("allSignals.mat");
Fs = 50e6; % Sampling frequency
T = 1/Fs; % Sampling period
L = 7500; % change as required
t = (0:L-1)*T; % Time vector
X = allSignals(1,:);
plot(t,X)
title("Signal ")
xlabel("t ")
ylabel("X(t)")
% fft
Y = fft(X);
L = length(X) % <— ADDED
L = 7500
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f,P1)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")
figure ; % after cut
X1 = allSignals(1,500:1100);
L1 = length(X1);
Y1 = fft(X1);
% P21 = abs(Y1/L1);
P21 = abs(Y1/L); % <— CHANGED
P11 = P21(1:L1/2+1);
Warning: Integer operands are required for colon operator when used as index.
P11(2:end-1) = 2*P11(2:end-1);
f1 = Fs*(0:(L1/2))/L1;
plot(f1,P11)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")
.
  2 个评论
KALEESH
KALEESH 2023-10-3
Indeed it worked ,one question how about zero padding in this case ? is it right to use in this case or when it should be used?
L = 2*length(x1);
Y1 = fft(X1,L); % instead of Y1 = fft(X1);
Star Strider
Star Strider 2023-10-3
Zero-padding is appropriate.
It would be better to use this:
L = length(X1);
NFFT = 2^nextpow2(L);
Y1 = fft(X1,NFFT);
or better yet, this:
Y1 = fft(X1(:).*hann(L),NFFT);
since the window function corrects for the fft being finite, providing a more accurate result, and a power-of-2 fft length significantly improves its efficiency. Zero-padding it also improves the frequency resolution.
.

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