Exam 1 Flashcards

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1
Q

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

A

True

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2
Q

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

A

False

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

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3
Q

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

A

4

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4
Q

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

A

Tangential signals

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5
Q

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

A

True

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6
Q

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

A

True

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6
Q

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

A

False

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

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7
Q

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

A

False

(series cascade)

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8
Q

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

A

True

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9
Q

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].

A

True

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10
Q

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

A

True

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11
Q

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

Commutative
Distributive
Conjunctive
Associative

A

Conjunctive

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12
Q

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

A

False

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

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13
Q

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

A

True

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14
Q

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

A

False

g[n] * h[n] = 𝝳[n]
x[n] * 𝝳[n] = x[n]

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15
Q

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

A

True

16
Q

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

A

False

(is called a recursive system.)

17
Q

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

A

True

18
Q

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

A

True

19
Q

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

A

Second order (largest delay)

20
Q

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

A

True

21
Q

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

A

True

22
Q

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

A

False

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

23
Q

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

A

False

N = period

24
Q

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)

A

Cos((π/2)n)

25
Q

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.

A

True

26
Q

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

A

True

27
Q

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

A

False

aₖbₖ

28
Q

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

A

True

29
Q

Class 9: DTFS and Filtering Whiteboard isnt posted in myCourses

A

True