EXERCISES

EXERCISES WITH SOLUTIONS

Exercise 1.1:

Write the following complex signals in polar form, that is, in the form x( t) = r( t) e ^j? ⁽ ^t ⁾, r( t), ?( t) ? ?, r( t) > 0 for continuous-time signals and x[ n] = r[ n] e ^j? ^[ ⁿ ^], r[ n], ?[ n] ? ? , r[ n] > 0 for discrete-time signals.


	x[ n] = nje ⁿ ⁺ ^j, n >0

Answers

Exercise 1.2:

Determine whether the following systems are: (1) memoryless, (2) time-invariant, (3) linear, (4) causal, or (5) BIBO stable. Justify your answers.

	y[ n] = x[1 - n]

	y( t) = tx( t)
	y[ n] = x[ n- k]

Answers

Memoryless? No. For example, the output y[0] = x[1] depends on a future value of the input.
Time-invariant? No.
Linear? Yes. Let y ₁[ n]:= Sx ₁[ n] = x ₁[1 -n], y ₂[ n]:= Sx ₂[ n] = x ₂[1- n].Then, the output of the system with x[ n] := ? x ₁ [ n] + ?x ₂ [ n] is...

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Fundamentals of Signals and Systems

TABLE OF CONTENTS

EXERCISES

EXERCISES WITH SOLUTIONS

Exercise 1.1:

Exercise 1.2:

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