Exam 1 Flashcards
A discrete-time signal x[n] is only defined for integer values of the independent variable n
True
The discrete-time unit impulse signal 𝝳[n] is 0, for n=0 and 1 for all other values of n ≠ 0
False
(𝝳[n] is 1, for n=0 and 0 for all other values of n ≠ 0)
The period of x[n] = cos((π/2)n) is
(2, 4, π/2, 8)
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
Tangential signals
If you double the input to a linear system, the output will also be doubled.
True
The output of a causal system only depends on future values of the input.
False
(only depends on present & past values of the input)
If you delay the input to a time-invariant system by 5 samples, the output will also be delayed by 5 samples.
True
The system below illustrates a parallel connection of the systems S1 and S2
-> [S1] -> [S2] ->
False
(series cascade)
The associative property of convolution states that x[n](h[n]g[n]) = (x[n]h[n])g[n]
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
x[n] * (h₁[n] + h₂[n]) = x[n] * h₁[n] + x[n] * h₂[n]
True
Which of the following properties of convolution is NOT covered in the reading and videos
Commutative
Distributive
Conjunctive
Associative
Conjunctive
If an LTI system is causal, then the impulse response h[n] = -1 for n<0
False
(then the impulse response h[n] = 0 for n<0)
If an LTI system is stable, then the impulse response satisfies sum(n=-infinity to infinity)abs(h[n])<infinity
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
False
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
A difference equation which uses earlier values of the output to compute the current value of the output is called a divergent system.
False
(is called a 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
1. Adding two signals
2. Multiply by a constant (gain)
3. A delay
True
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
Second order (largest delay)
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
True
If x[n] is periodic with period N, the fundamental frequency of the signal is ω₀ = 2π/N
True
The discrete-time Fourier series represents a periodic discrete-time signal x[n] as a sum of scaled and shifted unit impulses.
False
(x[n] as a sum of scaled complex exponentials.)
The discrete-time Fourier series requires an infinite sum of harmonics to represent a periodic signal x[n]
False
N = period
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)
Cos((π/2)n)
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.
True
The Fourier series for y[n] = x[n-m] is bₖ = (e^(-jk(2π/N)m))aₖ
True
If you convolve x[n] with y[n], then you also convolve their Fourier series aₖ and bₖ
False
aₖbₖ
The Fourier series for the sum of the two signals x[n] +y[n] is the sum aₖ + bₖ
True
Class 9: DTFS and Filtering Whiteboard isnt posted in myCourses
True
