Compute the Fourier Transform for: x(n)=u(n)-u(n-6); x(n)=[(2^n)*u]*(-n); x(n)=[-2,-1,0,1,2]

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For the first equation:
x=[1 0 0 0 0 0 -1];
y=fft(x)
y =
Columns 1 through 3
0.0000 + 0.0000i 0.3765 - 0.7818i 1.2225 - 0.9749i
Columns 4 through 6
1.9010 - 0.4339i 1.9010 + 0.4339i 1.2225 + 0.9749i
Column 7
0.3765 + 0.7818i
But thats all I can solve, the other 2 equations need help....Thanks!

Answers (1)

Sharmin Kibria
Sharmin Kibria on 25 Jun 2021
Hello,
I believe you are trying to calculate the Fourier Transform of the three signals.
x[n] = u[n]-u[n-6] = 1, n = 0,1,...5, x[n] = 0 otherwise
x[n] = (2^n)u[-n]
x[n] = [-2 -1 0 1 2]
You should be able to calculate the FFT for the third signal directly. For the first two signals you need to theorically calculate the values of x[n] from the definition of unit step function. Once you know the values of x[n], you can calculate the FFT for these signals.
Thanks
Sharmin

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