Exam 1 (Class 2-7) Flashcards
A discrete-time signal x[n] is only defined for integer values of the independent variable n
True/False
True
The discrete-time unit impulse signal δ[n] is 0, for n = 0 and 1 for all other values of n =/= 0
True/False
False
0 for n = 0,
1 for all other values n =/= 0
The discrete-time unit impulse signal δ[n] is 1, for n = 0 and 0 for all other values of n =/= 0
True/False
True
The period of x[n] = cos((π/2)n) is
a) 2
b) 4
c) π/2
d) 8
b) 4
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
d) tangential signals
If you double the input to linear system, the output will also be doubled
True/False
True
The output of a causal system only depends on the future values of the input
True/False
False
Present and past values
If you delay the input to a time-invariant system by 5 samples, the output will also be delayed by 5 samples
True/False
True
The system below illustrates a parallel connection of the systems S1 and S2
→[ S1 ]→[ S2 ]→
True/False
False
This is a series connection
The associative property of convolution states that
x[n](h[n]g[n]) = (x[n]h[n])g[n]
True/False
True
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
True
The associative property of convolution states that
x[n](h1[n]+h2[n]) = x[n]h1[n]+x[n]*h2[n]
True/False
True
Which of the following properties of convolution is NOT covered in the reading and videos
a) commutative
b) distributive
c) conjunctive
d) associative
c) conjunctive
If an LTI system is causal, then the impulse response h[n] = -1 for n < 0
True/False
False
h[n] = 0 for n < 0
If an LTI system is stable, then the impulse response satisfies
∞
Σ | h[n] | < ∞
n=-∞
True/False
True
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
False. It doesn’t work like that.
But…
g[n] ∗ h[n] = δ[n]
x[n] ∗ δ[n] = x[n]
The unit step response of an LTI system is defined to be s[n] = u[n] ∗ h[n] where ∗ is convolution
True/False
True
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
False.
Recursive System.
Initial rest auxiliary conditions guarantee that a system satisfying a linear, constant-coefficient difference equation will be causal, linear, and time-invariant
True
The elements required to make a block diagram of a discrete-time linear constant-coefficient difference equation are:
- Adding two signals
- Multiplying by a constant (gain)
- Delaying a signal
True/False
True
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
b) Second order
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
True
If x[n] is periodic with period N, the fundamental frequency of the signal is ω0 = 2π/N
True/False
True
The discrete-time Fourier series represents a periodic discrete-time signal x[n] as a sum of scaled and shifted unit impulses
True/False
False.
scaled complex exponentials
The discrete-time Fourier series requires an infinite sum of harmonics to represent a periodic signal x[n]
True/False
False.
N = period
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)
c) cos((π/2)n)
