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

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

Answer 6

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

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

Answer 7

False

(series cascade)

Question 8

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

Answer 8

True

Question 9

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 9

True

Question 10

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

Answer 10

True

Question 11

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

Commutative
Distributive
Conjunctive
Associative

Answer 11

Conjunctive

Question 12

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

Answer 12

False

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

Question 13

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

Answer 13

True

Question 14

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 14

False

g[n] * h[n] = 𝝳[n]
x[n] * 𝝳[n] = x[n]

Question 15

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

Answer 15

True

Question 16

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

Answer 16

False

(is called a recursive system.)

Question 17

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

Answer 17

True

Question 18

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 18

True

Question 19

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 19

Second order (largest delay)

Question 20

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 20

True

Question 21

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

Answer 21

True

Question 22

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

Answer 22

False

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

Question 23

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

Answer 23

False

N = period

Question 24

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 24

Cos((π/2)n)

Question 25

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 25

True

Question 26

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

Answer 26

True

Question 27

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

Answer 27

False

aₖbₖ

Question 28

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

Answer 28

True

Question 29

Class 9: DTFS and Filtering Whiteboard isnt posted in myCourses

Answer 29

True