Final Flashcards

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1
Q

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

A

False

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2
Q

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

A

True

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3
Q

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

A

False
interpolation, reconstruction

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4
Q

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

A

D: T = 1/3000

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

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5
Q

Cos(x) is equal to

A

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

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6
Q

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

A

True

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7
Q

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.

A

False
Will be a lowpass filter as well.

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8
Q

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

A

True

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9
Q

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

A

True

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10
Q

Sin(x) is equal to

A

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

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11
Q

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

A

B. Taking the derivative of a signal

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12
Q

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

A

True

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13
Q

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

A

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

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14
Q

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

A

True

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15
Q

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

A

False

Not the derivative but samples

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16
Q

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

A

True

17
Q

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

A

True.

18
Q

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

A

False

Not less than but > or equal to.

19
Q

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

A

True

20
Q

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.

A

True

21
Q

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

A

True

22
Q

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

A

True

23
Q

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

A

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

24
Q

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

A

True