how to claculate fft with window function?

Question

Jack Daniels 2022-11-9

0
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https://ww2.mathworks.cn/matlabcentral/answers/1847238-how-to-claculate-fft-with-window-function

评论： Star Strider 2022-11-10

I saw several code implementation fft with window fcn.

size(window)
ans =
1       44100
size(z)
ans =
1       44100
% calculate fft
z = fft(s.*window);

or

size(x)
ans =
1        1001
size(winvec)
ans =
1001           1
xdft = fft(x'.*winvec);

How it should be calculated fft argument by column product or row product?

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Answer 1

Star Strider 2022-11-9

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https://ww2.mathworks.cn/matlabcentral/answers/1847238-how-to-claculate-fft-with-window-function#answer_1095463

在 MATLAB Online 中打开

The first is correct. Note that ‘s’ needs to be a column vector.

Fs = 1000;

L = 1E+4;

t = linspace(0, L-1, L).'/Fs; % Column Vector

s = sum(sin([1;100;200;300;400]*2*pi*t.')).'; % Column Vector

figure

plot(t, s)

grid

Fn = Fs/2;

NFFT = 2^nextpow2(L);

FTs = fft(s,NFFT)/L;

Fv = linspace(0, 1, NFFT/2+1)*Fn;

Iv = 1:numel(Fv);

figure

plot(Fv, abs(FTs(Iv)))

grid

xlabel('Frequency')

ylabel('Magnitude')

title('Without Window')

FTs = fft(s.*hamming(L),NFFT)/L;

figure

plot(Fv, abs(FTs(Iv)))

grid

xlabel('Frequency')

ylabel('Magnitude')

title('With Window')

.

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Jack Daniels 2022-11-10

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Can be written somehow differently?

t = linspace(0, L-1, L).'/Fs;                       % Column Vector
s = sum(sin([1;100;200;300;400]*2*pi*t.')).';       % Column Vector

It seems unreadable ... " .' " - what that mean in the of the statement?

Thanks for explanantion.

Star Strider 2022-11-10

在 MATLAB Online 中打开

My pleasure!

The code creates a time vector and then a signal vector by summing the rows of ‘s’, creating column vectors.

A slightly easier approach would have been:

t = linspace(0, L-1, L)/Fs;                       % Row Vector
s = sum(sin([1;100;200;300;400]*2*pi*t)).'        % Column Vector
t = t(:);                                         % Column Vector

The (.') is the simple transpose operator, with (') being the complex conjugate transpose operator. For real arrays there’s no difference, however most of us here have gotten used to specifying the simple transpose and complex conjugate transpose to avoid the unintended consequences of using the complex conjugate transpose when we intended to use the simple transpoise.

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