Need help with Fourier Transform of a function

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

[Abdelrhman Abdelfatah]

I edited the question as It was not as clear.

Answer 1

[Madhu Varshini]

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)