Question

BC:9.2 Find the discrete time Fourier transform (DTFT) for the following sampled time signals. (Hint use the tables of DTFT pairs and DTFT properties) a.) $x_a[n] = (0.3e^{j0.15pi})^{n+2} u[n+3]$ b.) $x_b[n] = ext{rect}left(frac{n-3}{8} ight)$ c.) $x_c[n] = ext{rect}left(frac{n-3}{8} ight)delta[n+2]$ d.) $x_d[n] = ext{rect}left(frac{n-3}{8} ight) * sum_{k=-infty}^{infty} delta[n-20k]$ e.) $x_e[n] = (-0.2)^n cos(0.65pi n)u[n]$

          BC:9.2 Find the discrete time Fourier transform (DTFT) for the following sampled time signals. (Hint use the tables of DTFT pairs and DTFT properties)
a.)
$x_a[n] = (0.3e^{j0.15pi})^{n+2} u[n+3]$
b.)
$x_b[n] = 	ext{rect}left(frac{n-3}{8}
ight)$
c.)
$x_c[n] = 	ext{rect}left(frac{n-3}{8}
ight)delta[n+2]$
d.)
$x_d[n] = 	ext{rect}left(frac{n-3}{8}
ight) * sum_{k=-infty}^{infty} delta[n-20k]$
e.)
$x_e[n] = (-0.2)^n cos(0.65pi n)u[n]$

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$BC:9.2 Find the discrete time Fourier transform (DTFT) for the following sampled time signals. (Hint use the tables of DTFT pairs and DTFT properties) a.) xa[n] = (0.3e^j0.15pi)^n+2 u[n+3] b.) xb[n] = extrectleft(fracn-38 ight) c.) xc[n] = extrectleft(fracn-38 ight)delta[n+2] d.) xd[n] = extrectleft(fracn-38 ight) * sumk=-infty^infty delta[n-20k] e.) xe[n] = (-0.2)^n cos(0.65pi n)u[n]$

Added by Juan Manuel H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/17/2023

Step 1

3ej0.15r ` u[n + 3]. We can see that it is a product of two signals, one is a shifted unit step signal and the other is a complex exponential signal. Using the time shifting property of DTFT, we can shift the unit step signal by 3 to get u[n+3] and using the Show more…

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BC: 9.2 Find the discrete-time Fourier transform (DTFT) for the following sampled time signals (Hint: use the tables of DTFT pairs and DTFT properties) a.) x_a[n] = (0.3e^{j0.15pi})^{n+2} u[n + 3] b.) x_b[n] = rect((n-3)/8) c.) x_c[n] = rect((n-3)/8) δ[n+2] d.) x_d[n] = rect((n-3)/8) * ∑_{k=-∞}^{∞} δ[n-20k] e.) x_e[n] = (-0.2)^n cos(0.65πn) u[n]

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