Exam 2 Flashcards
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.
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
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]
True
Discrete time LTI systems designed to remove some frequencies from a signal while leaving other frequencies unchanged are known as frequency modulation systems
False
frequency selective fillers
The region from -pi/4 < w < pi/4 in the frequency response below is the passband of the filter.
False
Cant add an image but what is shown is the stopband (empty space between two bands).
The frequency response shown below is an example of a DT lowpass filter
False
Once again cant add images but its a bandpass(2 passes in between -pi and pi
The DTFT says we can construct any x[n] from the weighted sum of N complex exponentials even if x[n] is not periodic
False
sum of all complex exponentials from -pi to pi
Every DTFT is periodic in frequency with period 2pi i.e.,
X(e^(jw)) = X(e^(j(w+2pi))
True
The DTFT of x[n] converges if
Summation from n = -infinity to infinity(abs(x[n]) < infinity)
The continuous unit impulse function delta(t) is best defined by what it does inside an integral.
True
Multiplying X(e^(jw)) and Y(e^(jw)) corresponds to convolving x[n] with y[n].
True
Shifting a signal in time equivalent to multiplying its Fourier transform by a complex exponential.
True
If y[n] = ax[n] then Y(e^(jw)) = aX(e^(jw))
True
If x[n] is real, then its Fourier transform X(e^(jw)) is conjugate odd symmetric, ie., X(e^(jw)) = X*(e^(-jw))
False
odd X(e^(jw)) = + X*(e^(-jw))
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)
2cos((pi/2)n)
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))
False
Y(e^(jw)) = X(e^(jw)) * H(e^(jw))
The frequency response of an LTI system H(e^(jw)) is the Fourier transform of the system’s impulse response h[n].
True
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.
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.
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]
True
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)
sin(x)
The impulse response of an ideal DT lowpass filter with cutoff frequency omeganot(wo) is
cos(won)/(pin)^2
False
sin(won)/(pin) = h[n]
The magnitude of the frequency response |H(e^(jw)| tells us how a filter amplifies or attenuates each frequency in the signal.
True
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
B
The causal first order system y[n] -ay[n-1] = x[n]
has impulse response
h[n] = a * delta[n-1]
False
h[n] = (a^n)u[n]
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]
False
h[n] = (r^n)sin((n+1)theta)u[n]/(sin(theta))
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.
True
The reading and videos include an example showing lowpass filtering for weekly temperature data for Boston
False
really hoping this one is on the exam
All continuous time signals can be completely represented by discrete time samples
False
Infinite number of frequency to specify a discrete time signal 0.000000000000000000000000000000000000000000000000000000000000000000… precision you know.
Aliasing occurs when the sampling frequency is less than two times the highest frequency in the continuous time signal
True
Fitting a continuous time signal to a set of discrete samples is known as hybridization
False
interpolation, reconstruction
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
D.
Euler Identity for cos(x) is?
bruh.
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.
