EXAM 1 RAT 1-7

Question 1

If x(t) is a periodic signal with period T, it satisfies x(t) = 2x(t+T/2).

Answer 1

False

Question 2

An even symmetric signal satisfies the equation x(t) = -x(-t)

Answer 2

False

Question 3

The unit step u(t) is 1 for t > 0 and 0 for t < 0.

Answer 3

True

Question 4

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

Answer 4

True

Question 5

The output of a causal system only depends on current and past values of the input.

Answer 5

True

Question 6

If you delay the input to a time-invariant system by 2 seconds, the output will also be delayed by 2 seconds.

Answer 6

True

Question 7

The impulse response h(t) of an LTI system is the output observed when the input x(t)=δ(t), the unit impulse function.

Answer 7

True

Question 8

We can build any signal x(t) as a finite sum of weighted and shifted unit step functions u(t).

Answer 8

False

Question 9

The verb form of convolution is “convolute”, as in “The problem required that we convolute x(t) with h(t).”

Answer 9

False

Question 10

If we know the impulse response h(t) of an LTI system, the convolution integral allows us to find the output y(t) for any input x(t).

Answer 10

True

Question 11

If an LTI system with impulse response h(t) is stable, then the impulse response is bounded by 1 for all time, i.e., |h(t)|<1.

Answer 11

False

Question 12

Convolution is associative, i.e., (x(t) h1(t)) h2(t) = x(t) (h1(t) h2(t))

Answer 12

True

Question 13

If two LTI systems are inverses of each other, than their impulse responses h(t) and g(t) satisfy h(t) + g(t) = 1

Answer 13

False

Question 14

If an LTI system is causal, then h(t) = 0 for t<0.

Answer 14

True

Question 15

The differential equation below is fourth order

(d^3 y(t)/dt^3) + (d^2 y(t)/ dt^2) - 2(dy(t)/dt) + 9y(t) = 2x(t) + 4(d^2 x(t)/ dt^2)

Answer 15

False

Question 16

Initial rest conditions guarantee that the solution to a linear constant-coefficient differential equation will be linear and time invariant.

Answer 16

True

Question 17

Which of the elements below is NOT required to draw a block diagram of a causal CT LTI system

A) Gain

B) Exponential

C) Integrator

D) Adder

Answer 17

B) Exponential

Question 18

If the signal x(t) is periodic with period T, is has a fundamental frequency ω0 = 2π/T.

Answer 18

True

Question 19

If the input to an LTI system is x(t) = 4e^2t then the output must be y(t) = 2e^4t

Answer 19

False

Question 20

The continuous-time Fourier series represents a periodic signal x(t) with period T as a weighted sum of complex exponentials with frequencies k(2π/T).

Answer 20

True

Question 21

The CT Fourier series can represent any periodic signal with period T using only T harmonic frequencies.

Answer 21

False