Exam 1

Question 1

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

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

Answer 2

False

(𝝳[n] is 1, for n=0 and 0 for all other values of n ≠ 0)

Question 3

The period of x[n] = cos((π/2)n) is
(2, 4, π/2, 8)

Answer 3

4

Question 4

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

The unit step u[n]
The unit impulse 𝝳[n]
Exponential signals
Tangential signals

Answer 4

Tangential signals

Question 5

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

Answer 5

True

Question 6

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

Answer 6

False

(only depends on present & past values of the input)

Question 7

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

Answer 7

True

Question 8

The system below illustrates a parallel connection of the systems S1 and S2
-> [S1] -> [S2] ->

Answer 8

False

(series cascade)

Question 9

The associative property of convolution states that x[n](h[n]g[n]) = (x[n]h[n])g[n]

Answer 9

True

Question 10

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].

Answer 10

True

Question 11

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

Answer 11

True

Question 12

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

Commutative
Distributive
Conjunctive
Associative

Answer 12

Conjunctive

Question 13

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

Answer 13

False

(then the impulse response h[n] = 0 for n<0)

Question 14

If an LTI system is stable, then the impulse response satisfies sum(n=-infinity to infinity)abs(h[n])<infinity

Answer 14

True

Question 15

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

Answer 15

False

g[n] * h[n] = 𝝳[n]
x[n] * 𝝳[n] = x[n]

Question 16

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

Answer 16

True

Question 17

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

Answer 17

False

(is called a recursive system.)

Question 18

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

Answer 18

True

Question 19

The elements required to make a block diagram of a discrete-time linear constant-coefficient difference equation are
1. Adding two signals
2. Multiply by a constant (gain)
3. A delay

Answer 19

True

Question 20

What is the order of the linear constant-coefficient difference equation
y[n] + 2y[n-1] + 3y[n-2] = x[n] - x[n-1]

First order
Second order
Third order
Fourth order

Answer 20

Second order (largest delay)

Question 21

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

Answer 21

True

Question 22

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

Answer 22

True

Question 23

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

Answer 23

False

(x[n] as a sum of scaled complex exponentials.)

Question 24

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

Answer 24

False

N = period

Question 25

Euler’s identity allows us to rewrite
(1/2)e^(j(π/2)n) + (1/2)e^(-j(π/2)n)

Sin((π/2)n)
Cos((π/2)n)-Cos((-π/2)n)
Cos((π/2)n)
e^(j(π/2)n+(-π/2)n)

Answer 25

Cos((π/2)n)

Question 26

For all of today’s problems, assume that x[n] is a periodic signal with period N and Fourier series aₖ and y[n] is a periodic signal with the same period N and Fourier series bₖ.

If x[n] is real and even, then aₖ will be real.

Answer 26

True

Question 27

The Fourier series for y[n] = x[n-m] is bₖ = (e^(-jk(2π/N)m))aₖ

Answer 27

True

Question 28

If you convolve x[n] with y[n], then you also convolve their Fourier series aₖ and bₖ

Answer 28

False

aₖbₖ

Question 29

The Fourier series for the sum of the two signals x[n] +y[n] is the sum aₖ + bₖ

Answer 29

True

Question 30

Class 9: DTFS and Filtering Whiteboard isnt posted in myCourses

Answer 30

True