Final

Question 1

All continuous time signals can be completely represented by discrete time signals.

Answer 1

False

Question 2

Aliasing occurs when the sampling frequency is less than two times the highest frequency in the continuous time signal.

Answer 2

True

Question 3

Fitting a continuous time signal to a set of discrete samples is known as hybridization.

Answer 3

False
interpolation, reconstruction

Question 4

Let xc(t) be a continuous time signal bandlimited to 2pi(1000).
Which sampling period T results in discrete samples x[n] = xc(nT) that capture all of the information in the original continuous time signal?
A: T = 1/1000
B: T = 2000
C: T = 1/500
D: T = 1/3000

Answer 4

D: T = 1/3000

2pi/T > 2(2pi(1000))

Question 5

Cos(x) is equal to

Answer 5

(1/2)e^(jx) + (1/2)e^(-jx)

Question 6

Dividing the time axis by T corresponds to multiplying the frequency axis by T.

Answer 6

True

Question 7

If there is no aliasing and the discrete-time system is a lowpass filter, then the overall continuous time system will be a highpass filter.

Answer 7

False
Will be a lowpass filter as well.

Question 8

Changing the sampling period T will change the overall continuous time filter frequency response Hc(jw).

Answer 8

True

Question 9

If there is no aliasing a system will be capable of acting like an LTI system as long as the discrete time system Hd(e^(jΩ)) is LTI

Answer 9

True

Question 10

Sin(x) is equal to

Answer 10

(1/(2j))e^(jx) - (1/(2j))e^(-jx)

Question 11

Which of the following elements is NOT required to construct a block diagram of a linear constant coefficient difference equation.

A. Scaling a signal by a constant
B. Taking the derivative of a signal
C. Delaying a signal by one sample
D. Adding two signals

Answer 11

B. Taking the derivative of a signal

Question 12

The frequency response generally increases in the region of the unit circle close to a pole, and decreases close to a zero.

Answer 12

True

Question 13

How do you count the order of a block diagram of a linear constant coefficient difference equation?

Answer 13

Count the number of delays (i.e. z^-1)

Question 14

Series combination looks like two systems getting combined together like a train in a block diagram of a linear constant coefficient difference equation,

Answer 14

True

Question 15

The Discrete Fourier Transform X[k] is the derivative of X(e^(jw)) with respect to w.

Answer 15

False

Not the derivative but samples

Question 16

One common use of the Discrete Fourier Transform is to approximate the Discrete Time Fourier Transform X(e^(jw)) for finite length data measurements.

Answer 16

True

Question 17

Sampling in the frequency domain corresponds to making periodic copies in the time domain.

Answer 17

True.

Question 18

To avoid aliasing in time, the DFT size N must be less than the length of the time domain signal x[n], M.

Answer 18

False

Not less than but > or equal to.

Question 19

Buck has forgotten to upload 3 Whiteboards worth of content for this set.

Answer 19

True

Question 20

Garret still doesn’t have the ability to upload images to Brainscape; thus he rephrased 2 questions that will give you the right idea when you see the problem on the exam.

Answer 20

True

Question 21

The z-transform of x[n-1] is z^-1X(z)

Answer 21

True

Question 22

The second order system
H(z) = 1 / (1 - (2rcos(θ)) z^-1 + r^2 z^-2)
will have peaks in the frequency response magnitude |H(e^jω)| near ω = ± θ

Answer 22

True

Question 23

Convolving in time corresponds to adding z-transforms, so if
y[n] = x[n]*h[n]
then
Y(z) = X(z)+H(z)

Answer 23

False
Y(z) = X(z) x H(z)
Convolution in time <-> Multiplication in frequency

Question 24

If an LTI system is causal and stable, then the system function H(z) must have all of its poles inside the unit circle.

Answer 24

True