Digital Signal Processing
Assignment 1: Discrete-time Signals & Systems
Note: You may use Matlab to solve the problems where necessary
All questions carry equal points
1. Is the sequence, absolutely summable?
2. Find the fundamental period of the sequence x[n] = cos(0.125nπ).
3. If x[n], y[n], and g[n] represent three finite-length sequences of lengths N, M, and L, respectively, with the first sample of each sequence occurring at n = 0, what is the length of the sequence ?
4. Evaluate the linear convolution of x[n] with itself, where x[n] = {1, 1}, 0 ≤ n ≤ 1.
5. Determine if the system described by y[n] = x[n+1] + x[n] + x[n-1] + x[n-2] is causal.
1
],
[
]
[
p
a
a
n
u
n
x
n
=
]
[
]
[
]
[
n
g
n
y
n
x
Ä
Ä