Exam 1 (Class 2-7)

Question 1

A discrete-time signal x[n] is only defined for integer values of the independent variable n

True/False

Answer 1

True

Question 2

The discrete-time unit impulse signal δ[n] is 0, for n = 0 and 1 for all other values of n =/= 0

True/False

Answer 2

False

0 for n = 0,
1 for all other values n =/= 0

Question 3

The discrete-time unit impulse signal δ[n] is 1, for n = 0 and 0 for all other values of n =/= 0

True/False

Answer 3

True

Question 4

The period of x[n] = cos((π/2)n) is

a) 2
b) 4
c) π/2
d) 8

Answer 4

b) 4

Question 5

Which of the following basic signals is NOT covered in the videos and reading

a) the unit step u[n]
b) the unit impulse δ[n]
c) exponential signals
d) tangential signals

Answer 5

d) tangential signals

Question 6

If you double the input to linear system, the output will also be doubled

True/False

Answer 6

True

Question 7

The output of a causal system only depends on the future values of the input

True/False

Answer 7

False

Present and past values

Question 8

If you delay the input to a time-invariant system by 5 samples, the output will also be delayed by 5 samples

True/False

Answer 8

True

Question 9

The system below illustrates a parallel connection of the systems S1 and S2

→[ S1 ]→[ S2 ]→

True/False

Answer 9

False

This is a series connection

Question 10

The associative property of convolution states that

x[n](h[n]g[n]) = (x[n]h[n])g[n]

True/False

Answer 10

True

Question 11

Knowing the impulse response h[n] for a linear, time-invariant system allows us to find the output y[n] for any input x[n]

True/False

Answer 11

True

Question 12

The associative property of convolution states that

x[n](h1[n]+h2[n]) = x[n]h1[n]+x[n]*h2[n]

True/False

Answer 12

True

Question 13

Which of the following properties of convolution is NOT covered in the reading and videos

a) commutative
b) distributive
c) conjunctive
d) associative

Answer 13

c) conjunctive

Question 14

If an LTI system is causal, then the impulse response h[n] = -1 for n < 0

True/False

Answer 14

False

h[n] = 0 for n < 0

Question 15

If an LTI system is stable, then the impulse response satisfies

∞
Σ | h[n] | < ∞
n=-∞

True/False

Answer 15

True

Question 16

If h[n] is the impulse response for an LTI system, and g[n] is the impulse response for the inverse system, then g[n] + h[n] = 0

True/False

Answer 16

False. It doesn’t work like that.

But…
g[n] ∗ h[n] = δ[n]
x[n] ∗ δ[n] = x[n]

Question 17

The unit step response of an LTI system is defined to be s[n] = u[n] ∗ h[n] where ∗ is convolution

True/False

Answer 17

True

Question 18

A difference equation which uses earlier values of the output to compute the current value of the output is called a divergent system

True/False

Answer 18

False.

Recursive System.

Question 19

Initial rest auxiliary conditions guarantee that a system satisfying a linear, constant-coefficient difference equation will be causal, linear, and time-invariant

Answer 19

True

Question 20

The elements required to make a block diagram of a discrete-time linear constant-coefficient difference equation are:

1. Adding two signals
2. Multiplying by a constant (gain)
3. Delaying a signal

True/False

Answer 20

True

Question 21

What is the order of the linear constant-coefficient difference equation shown below

y[n]+2y[n-1]+3y[n-2]=x[n]-x[n-1]

a) First order
b) Second order
c) Third order
d) Fifth order

Answer 21

b) Second order

Question 22

If the input to an LTI system is an exponential signal x[n] = z^n then the output must have the form y[n] = H(z) z^n

True/False

Answer 22

True

Question 23

If x[n] is periodic with period N, the fundamental frequency of the signal is ω0 = 2π/N

True/False

Answer 23

True

Question 24

The discrete-time Fourier series represents a periodic discrete-time signal x[n] as a sum of scaled and shifted unit impulses

True/False

Answer 24

False.

scaled complex exponentials

Question 25

The discrete-time Fourier series requires an infinite sum of harmonics to represent a periodic signal x[n]

True/False

Answer 25

False.

N = period

Question 26

Euler’s identity allows us to rewrite

(1/2)e^(j(π/2)n) + (1/2)e^(-j(π/2)n)

a) sin((π/2)n)
b) cos((π/2)n) - cos((-π/2)n)
c) cos((π/2)n)
d) e^(j(π/2)n+(-π/2)n)

Answer 26

c) cos((π/2)n)