Digital Signal Processing Quiz 2: 16 March 2025 (January 2025 term)

1. Consider a discrete time signal given below:

$x[n] = 4\delta[n+4] - 2\delta[n+3] + 3\delta[n+2] + 6\delta[n+1] + 3\delta[n] - 2\delta[n-1] + 4\delta[n-2]$

Evaluate the following without computing the DTFT.

a. $X\left(e^{j0}\right)$
b. $\angle X\left(e^{j\omega}\right)$
c. $X\left(e^{j\pi}\right)$
d. $\int_0^{2\pi} X\left(e^{j\omega}\right) d\omega$
e. $\int_0^{2\pi} \left|X\left(e^{j\omega}\right)\right|^2 d\omega$

[1 + 3 + 2 + 2 + 2]