Exam 2

Question 1

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.

Answer 1

True

Question 2

The Fourier series for y[n] = x[n-m] is bₖ = (e^(-jk(2π/N)m))aₖ

Answer 2

True

Question 3

If you convolve x[n] with y[n], then you also convolve their Fourier series aₖ and bₖ

Answer 3

False

aₖbₖ

Question 4

The Fourier series for the sum of the two signals x[n] +y[n] is the sum aₖ + bₖ

Answer 4

True

Question 5

The frequency response H(e^jw) for an LTI system tells us the gain to apply to each Fourier series coefficient ak of the periodic input signal x[n] to find the Fourier series coefficient bk for the output signal y[n]

Answer 5

True

Question 6

Discrete time LTI systems designed to remove some frequencies from a signal while leaving other frequencies unchanged are known as frequency modulation systems

Answer 6

False

frequency selective fillers

Question 7

The region from -pi/4 < w < pi/4 in the frequency response below is the passband of the filter

Answer 7

False

Cant add an image but what is shown is the stopband (empty space between two bands).

Question 8

The frequency response shown below is an example of a DT lowpass filter

Answer 8

False

Once again cant add images but its a bandpass(2 passes in between -pi and pi

Question 9

The DTFT says we can construct any x[n] from the weighted sum of N complex exponentials even if x[n] is not periodic

Answer 9

False

sum of all complex exponentials from -pi to pi

Question 10

Every DTFT is periodic in frequency with period 2pi i.e.,

X(e^(jw)) = X(e^(j(w+2pi))

Answer 10

True

Question 11

The DTFT of x[n] converges if

Answer 11

Summation from n = -infinity to infinity(abs(x[n]) < infinity)

Question 12

The continuous unit impulse function delta(t) is best defined by what it does inside an integral.

Answer 12

True

Question 13

Multiplying X(e^(jw)) and Y(e^(jw)) corresponds to convolving x[n] with y[n].

Answer 13

True

Question 14

Shifting a signal in time equivalent to multiplying its Fourier transform by a complex exponential.

Answer 14

True

Question 15

If y[n] = ax[n] then Y(e^(jw)) = aX(e^(jw))

Answer 15

True

Question 16

If x[n] is real, then its Fourier transform X(e^(jw)) is conjugate odd symmetric, ie., X(e^(jw)) = X*(e^(-jw))

Answer 16

False

odd X(e^(jw)) = + X*(e^(-jw))

Question 17

Which of the following is equal to e^(j(pi/2)n) + e^(-j(pi/2)n)
(1/2) cos(pi*n)
cos((pi/2)n)
2sin((pi/2)n)
2cos((pi/2)n)

Answer 17

2cos((pi/2)n)

Question 18

If the output of an LTI system is y[n] = x[n] * h[n], then the Fourier transform of the output is Y(e^(jw)) = X(e^(jw)) + H(e^(jw))

Answer 18

False

Y(e^(jw)) = X(e^(jw)) * H(e^(jw))

Question 19

The frequency response of an LTI system H(e^(jw)) is the Fourier transform of the system’s impulse response h[n].

Answer 19

True

Question 20

The examples in the reading and videos use reciprocal fractions to turn the sum of first order terms into a product of first order terms.

Answer 20

False

The examples in the reading and videos use partial fractions to turn the product of first order terms into a sum of first order terms.

Question 21

If the frequency response of a causal LTI system is
H(e^(jw)) = 1/(1-ae^(-jw))
Then the impulse response is
h[n] = (a^n)*u[n]

Answer 21

True

Question 22

Which of the following is equal to
(1/2j)e^(jx)-(1/2j)e^(-jx)
(1/2)sin(x)
cos(x/2)
sin(x)
cos(x)

Answer 22

sin(x)

Question 23

The impulse response of an ideal DT lowpass filter with cutoff frequency omeganot(wo) is
cos(won)/(pin)^2

Answer 23

False

sin(won)/(pin) = h[n]

Question 24

The magnitude of the frequency response |H(e^(jw)| tells us how a filter amplifies or attenuates each frequency in the signal.

Answer 24

True

Question 25

Which of the steps below is not part of the process of designing the impulse response of a causal FIR filter
A. Design the ideal filter impulse response for the desired filter
B. Flip the impulse response
C. Shift the impulse response to make it causal.
D. Truncate the impulse response to the desired length

Answer 25

B

Question 26

The causal first order system y[n] -ay[n-1] = x[n]
has impulse response
h[n] = a * delta[n-1]

Answer 26

False

h[n] = (a^n)u[n]

Question 27

The underdamped causal second-order discrete-time system
y[n] -2rcos(theta)y[n-1] +(r^2)y[n-2] =x[n]
has impulse response
h[n] = (r^n)u[n]

Answer 27

False

h[n] = (r^n)sin((n+1)theta)u[n]/(sin(theta))

Question 28

Depending on the coefficients of the difference equation, the impulse response of a second order system could be the sum of two decaying exponentials, or an oscillating sinusoid with an exponentially decaying envelope.

Answer 28

True

Question 29

The reading and videos include an example showing lowpass filtering for weekly temperature data for Boston

Answer 29

False

really hoping this one is on the exam

Question 30

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

Answer 30

False

Infinite number of frequency to specify a discrete time signal 0.000000000000000000000000000000000000000000000000000000000000000000… precision you know.

Question 31

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

Answer 31

True

Question 32

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

Answer 32

False
interpolation, reconstruction

Question 33

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 33

D.

Question 34

Euler Identity for cos(x) is?
bruh.

Answer 34

At this point if you don’t know it you gonna have a problem tomorrow. Like its on the formula sheet I don’t even know why he would ever potentially put this on the exam.