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]

Question

Li Hui Chew 2021-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/864345-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

回答： Sharmin Kibria 2021-6-25

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!

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Answer 1

Sharmin Kibria 2021-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/864345-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#answer_733650

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