Need help with Fourier Transform of a function

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Abdelrhman Abdelfatah
回答： Madhu Varshini 2022-6-10
Hello, I need to get fourier transorm of a function y(t) which is a byproduct of x(t) and some trig function.
my issue is that i don't know x(t), but i know x(wj) function .... so i need to plot y(t).. then y(jw) .. and here is what i have done so far
t=-1:0.001:1;
% Function I want to plot y(t) = x(t) [cos(t/2) + cos(3t/2)]
x_w=- abs(t)+1; %given function as X(wj)
x_t=ifft(x_w); % I try to get x(t) out of the given x(wj)
% I want also to plot y(wj)
Thank you in advance

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回答（1 个）

Madhu Varshini
Madhu Varshini 2022-6-10
For this case, it is not necessary to get x(t).
If y(t) = x(t) .[cos(t/2) + cos(3t/2)]
and if x(jw) is known , then using convolution , we can get Y(jw) directly.
And then using Inverse Fourier transform ,Y(t) can be derived.
Below is the code snippet:
t=-1:0.001:1;
x_w = - abs(t)+1;
% y_t = x_t [cos(t/2) + cos(3t/2)]
% Let z_t = cos(t/2) + cos(3t/2)
z_t= (cos(t./2) + cos(3*t./2))
z_w = fft(z_t)
% y_t = x_t * z_t
% y_w will be convolution of x_w and y_w
y_w = conv(x_w,z_w)
% y_t will be the inverse Fourier Transform of y_w
y_t = ifft(y_w)
% plot Y(jw) function
figure(1)
plot(y_w)
%plot Y(t) function
figure(2)
plot(y_t)

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