Question

5.21. Compute the Fourier transform of each of the following signals: (a) $x[n] = u[n - 2] - u[n - 6]$ (b) $x[n] = (\frac{1}{2})^{-n}u[-n - 1]$ (c) $x[n] = (\frac{1}{3})^{|n|}u[-n - 2]$ (d) $x[n] = 2^n \sin(\frac{\pi}{4}n)u[-n]$

          5.21. Compute the Fourier transform of each of the following signals:
(a) $x[n] = u[n - 2] - u[n - 6]$
(b) $x[n] = (\frac{1}{2})^{-n}u[-n - 1]$
(c) $x[n] = (\frac{1}{3})^{|n|}u[-n - 2]$
(d) $x[n] = 2^n \sin(\frac{\pi}{4}n)u[-n]$

5.21. Compute the Fourier transform of each of the following signals:
(a) x[n] = u[n - 2] - u[n - 6]
(b) x[n] = ((1)/(2))^-nu[-n - 1]
(c) x[n] = ((1)/(3))^|n|u[-n - 2]
(d) x[n] = 2^n sin((π)/(4)n)u[-n]

Added by Jeffery T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Umar Sohail Qureshi

Step 1

(a) x[n] = u[n-2] - u[n-6] To compute the Fourier transform of this signal, we can use the definition of the Fourier transform: X(jω) = Σ x[n]e^(-jωn) Show more…

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Thanks for your feedback!

Just solve for a and d, also plot |X(jÏ‰)| using a plotting software like Python for a and d. I am having trouble with the code. 5.21. Compute the Fourier transform of each of the following signals: (a) x[n] = u[n-2] - u[n-6] (b) x[n] = (-n)u[-n-1] (c) x[n] = |n|u[-n-2] (d) x[n] = 2sin(n)u[-n]