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Spring 2026

520.214 - Signals and Systems

Homework 2

Assigned 2/3/26

Due 2/12/26 11:59pm

Problem 1

(a) Determine and sketch the even and odd parts of the signal de-picted in Fig. 1. Label your sketches carefully.

Figure 1

(b) Determine and sketch the even and odd parts of the signal de-picted in Fig. 2. Label your sketches carefully.

Figure 2

Problem 2

In our lectures, we were introduced a number of general properties of systems. In particular, a system may or may not be

(1) Memoryless

(2) Time invariant

(3) Linear

(4) Causal

(5) Stable

Please determine which of these properties hold and which do not hold for each of the following continuous-time or discrete-time sys-tems. Justify your answers. In each example, y(t) or y[n] denotes the system output and x(t) or x[n] is the system input.

(a) y(t) = [cos(3t)] · x(t)

(b) 

(c) y(t) = x(t/3)

(d) y[n] = nx[n]

(e) y[n] = Ev{x[n − 1]} = Even part of x[n − 1]

(f) 

Problem 3

Determine if each of the following systems is invertible. If so, find the inverse system; if not, justify why.

(a) y(t) = x(2t)

(b) 

(c) y[n] = nx[n]

(d) 

Problem 4

Consider the systems H, G, and F defined in Fig. 3

Figure 3

The systems in Fig. 4 are formed by parallel and cascade combina-tions of H, G, and F.

First, for each system in Fig. 4, express the output y[n] as a function of the input x[n].

Second, please answer which of these systems in Fig. 4 are equiva-lent?

Figure 4