314 exam 2
A LTI system described by the following differential equation: y'(t) + 2 y(t)= 8 x(t) What is the phase response of the system frequency response ∠H(ω) at ω=17 rad/s (in Degrees)?
-83.290
A LTI system described by the following differential equation: y'(t) + 2 y(t)= 6 x(t) What is the system impulse response h(t) at t= -2.64 seconds?
0
A LTI system described by the following differential equation: y'(t) + 5 y(t)= 5 x(t) What is the system impulse response h(t) at t= -1.97 seconds?
0
A LTI system described by the following differential equation: y'(t) + 5 y(t)= 7 x(t) What is the system impulse response h(t) at t= -6.98 seconds?
0
Consider a LTI system with frequency response given by: where ωc = 7 rad/s. Find the output y(t) of the system if the input x is given by: x(t) = 1 + 2cos(2t) + 2cos(4t) + 0.5 cos (6t)
0
For 𝑥(𝑡)=6 cos(10𝜋𝑡) + 5 cos(20𝜋𝑡), the Fourier series coefficient (ak) at k=0 is _____________
0
A LTI system described by the following differential equation: y'(t) + 9.6 y(t)= 14 x(t) What is the system impulse response h(t) at t= 0.73 seconds?
0.013
A LTI system described by the following differential equation: y'(t) + 8 y(t)= 2 x(t) What is the magnitude of the system frequency response |H(ω)| at ω=13 rad/s?
0.131
A LTI system described by the following differential equation: y'(t) + 8 y(t)= 3 x(t) What is the magnitude of the system frequency response |H(ω)| at ω=18 rad/s?
0.152
A LTI system described by the following differential equation: y'(t) + 6 y(t)= 8 x(t) What is the magnitude of the system frequency response |H(ω)| at ω=16 rad/s?
0.468
Consider a LTI system with frequency response given by: where ωc = 5 rad/s. Find the output y(t) of the system if the input x is given by: x(t) = 1 + 2cos(2t) + 2cos(4t) + 0.5 cos (6t)
0.5 cos (6t)
If y(t) = x(t)e−j5πt, where x(t) is the square wave shown below. The Fourier series coefficients (Yk) of y(t) is_________
0.5 sinc(0.5(k+5))
If y(t) = x(t)e−j5πt, where x(t) is the square wave shown below. The magnitude of the Fourier series coefficients (|Yk|) of y(t) is_________
0.5 sinc(0.5k)
The Fourier series coefficients (Xk) of the square wave shown below x(t) is.
0.5 sinc(0.5k)
If y(t) = x(t+0.5), where x(t) is the square wave shown below. The Fourier series coefficients (Yk) of y(t) is_________
0.5 sinc(0.5k) e+j0.5kπ
If y(t) = x(t+0.5), where x(t) is the square wave shown below. The Fourier series coefficients (Yk) of y(t) is_________
0.5 sinc(0.5k) e^(+j0.5kπ)
If y(t) = x(t−0.5), where x(t) is the square wave shown below. The Fourier series coefficients (Yk) of y(t) is_________
0.5 sinc(0.5k) e−j0.5kπ
x(t) is the square wave shown below. The Fourier series coefficients (Xk) of x(t) is_________
0.5 sinc(0.5k) e−j0.5kπ
A LTI system described by the following differential equation: y''(t)+ 11 y'(t) + 9 y(t)= 10 x'(t) +10 x(t) What is the magnitude of the system frequency response |H(ω)| at ω=8 rad/s?
0.776
A LTI system described by the following differential equation: y''(t) + 8 y(t)= 8 x(t) What is the system frequency response H(ω) at ω=0?
1
For x(t)= 2sinc(2𝑡-10), find the bandwidth in Hz?
1
Consider a LTI system with frequency response given by: where ωc = 3π rad/s. Find the output y(t) of the system if the input x is given by: x(t) = 1 + 2cos(2πt) + 2cos(4πt) + 0.5 cos (6πt)
1 + 2cos(2πt)
For the periodic signals below, which signal(s) has (have) real value for Fourier series coefficients (ak) ?
1, 3, 4, 8
For the periodic signals below, which one(s) does (do) have Fourier series coefficients (ak) with conjugate symmetry?
1,2,3,4,5,6,7,8,9
For the periodic signals below, which ones have the exact same magnitude response (|ak|) ?
1,2,4,5
A LTI system described by the following differential equation: y''(t)+ 10 y'(t) + 7 y(t)= 11 x'(t) +9 x(t) What is the system frequency response H(ω) at ω=0?
1.286
For a periodic signal 𝑥(𝑡)=6t, 0 < t <1.The 1st harmonic power is _____________
1.82378
For x(t)= 2sinc(10𝑡-3), find the Nyquist Rate in Hz?
10
For x(t)= 2sinc(10𝑡-6), find the Nyquist Rate in Hz?
10
For x(t)= 2sinc(3𝑡-4), find the Nyquist Rate in rad/s?
18.85
For 𝑥(𝑡)=7 cos(10𝜋𝑡) + 4 cos(20𝜋𝑡), the Fourier series coefficient (ak) at k=2 is _____________
2
For the periodic signals below, which signal(s) has (have) imaginary value for Fourier series coefficients (ak) ?
2, 5, 6
For a periodic signal 𝑥(𝑡)=3t, 0 < t <1.The DC power is _____________
2.25
For a periodic signal 𝑥(𝑡)=7t, 0 < t <1.The 1st harmonic power is _____________
2.482
Consider a LTI system with frequency response given by: where ωc = 3 rad/s. Find the output y(t) of the system if the input x is given by: x(t) = 1 + 2cos(2t) + 2cos(4t) + 0.5 cos (6t)
2cos(4t) + 0.5 cos (6t)
A LTI system described by the following differential equation: y''(t)+ 14 y'(t) + 3 y(t)= 11 x'(t) +9 x(t) What is the system frequency response H(ω) at ω=0?
3
A LTI system described by the following differential equation: y'(t) + 10 y(t)= 3 x(t) What is the system impulse response h(t) at t=0?
3
For the periodic signals below, which signal(s) has (have) a non-zero DC component for Fourier series coefficient (a0) ?
3, 7, 8, 9
For x(t)= 5cos(2𝜋𝑡)+2sin(4𝜋𝑡)−cos(7𝜋𝑡), find the bandwidth in Hz?
3.5
For a periodic signal 𝑥(𝑡)=6𝑠𝑖𝑛(𝜋𝑡), 0 < t <1.The Fourier series coefficient (ak) at k=0 is _____________
3.8197
A LTI system described by the following differential equation: y'(t) + 5 y(t)= 4 x(t) What is the system impulse response h(t) at t=0?
4
For x(t)= 2sinc(4𝑡-9), find the Nyquist Rate in Hz?
4
For a periodic signal 𝑥(𝑡)=7𝑠𝑖𝑛(𝜋𝑡), 0 < t <1.The Fourier series coefficient (ak) at k=0 is _____________
4.459
For a periodic signal 𝑥(𝑡)=9t, 0 < t <1.The Fourier series coefficient (ak) at k=0 is _____________
4.5
For 𝑥(𝑡)=3 cos(10𝜋𝑡) + 9 cos(20𝜋𝑡), the Fourier series coefficient (ak) at k=2 is _____________
4.50
For x(t)= 2sinc(10𝑡-7), find the bandwidth in Hz?
5
For x(t)= 5cos(2𝜋𝑡)+2sin(3𝜋𝑡)−cos(10𝜋𝑡), find the bandwidth in Hz?
5
For x(t)= 2sinc(9𝑡-4), find the Nyquist Rate in rad/s?
56.52
For 𝑥(𝑡)=7 cos(10𝜋𝑡) + 5 cos(20𝜋𝑡) + 6, the Fourier series coefficient (ak) at k=0 is _____________
6
For x(t)= 2sinc(10𝑡-7), find the Nyquist Rate in rad/s?
62.8
For x(t)= 2sinc(7𝑡-5), find the Nyquist Rate in Hz?
7
For x(t)= 5cos(2𝜋𝑡)+2sin(3𝜋𝑡)−cos(7𝜋𝑡), find the Nyquist Rate in Hz?
7
A function can be both time limited and bandlimited.
False
An anti-aliasing filter is a digital filter
False
For Fourier Series of a real-valued signal x(t), the power of the 1st harmonic is |a1|2
False
For Fourier Series, if x(t) is real and even, the Fourier Series coefficients (ak) will have an imaginary value.
False
For Fourier Series, if x(t) is real and odd, the Fourier Series coefficients (ak) will have a real value.
False
For Fourier series, the term in the summation for k = 0 is known as the fundamental frequency components or first harmonic components, and have the fundamental frequency ω0.
False
Fourier transform can be thought of as the limit of the Fourier series as the period approaches zero.
False
If we use an anti-aliasing filter before the sampling there will be no distortion in the recovered signal
False
If 𝑥(𝑡) is bandlimited to 𝐵 Hz then 𝑥(𝑡) can be perfectly recovered from it's samples provided that T𝑠 > 0.5/𝐵.
False
If 𝑥(𝑡) is bandlimited to 𝐵 Hz then 𝑥(𝑡) can be perfectly recovered from it's samples provided that 𝑓𝑠 <2𝐵.
False
In signal reconstruction, aliasing refers to reconstructing the wrong signal because of oversampling
False
Sampling is the process by which a signal is converted from continuous amplitude to discrete amplitude.
False
The Nyquist rate for sampling this signal 3cos(2𝜋𝑡)+2sin(4𝜋𝑡) should be 2 Hz
False
The sampling rate 𝑓𝑠 =0.5𝐵 is known as the Nyquist rate.
False
Time expansion of a signal x(t) to x(at) by an expansion factor a < 1, leads to expansion of its spectrum X(ω) to X(aω);
False
When we compress a function x(t), its Fourier transform X(ω) will compress as well.
False
The duality between the time domain and the ω-domain means that if a rectangular pulse in the time domain generates a sinc pattern in the frequency domain, then a sinc pulse in the time domain generates a rectangular spectrum in the frequency domain
True
The sampling rate 𝑓𝑠 =2𝐵 is known as the Nyquist rate.
True
For Fourier series, the magnitude spectrum of a real function is always ____________
even
For Fourier Series, if x(t) is real-valued, then Fourier series coefficients will follow |a−k|= −|ak|
false
If y(t) = x(t+0.5)−x(t−0.5), where x(t) is the square wave shown below. The Fourier series coefficients (Yk) of y(t) is_________
j sinc(0.5k) sin(0.5kπ)
For Fourier series, the phase spectrum of a real function is always ____________
odd
If x(t) = 3cos(2𝜋𝑡)+2sin(3𝜋𝑡)−cos(4𝜋𝑡) is sampled at a 200 Hz rate,
the signal will be oversampled
If x(t) = cos(400πt) is sampled at a 500 Hz rate,
the signal will be oversampled
If x(t) = 3cos(2𝜋𝑡)+2sin(3𝜋𝑡)−cos(4𝜋𝑡) is sampled at a 2 Hz rate,
the signal will be undersampled
For Fourier series, the terms in the summation for k = 1 and k = -1 are known as the fundamental frequency components or first harmonic components, and have the fundamental frequency ω0.
true
For Fourier series, the terms in the summation for k = K and k = -K are called the Kth harmonic components, and have the frequency Kω0.
True
For a time limited signal, if we use an anti-aliasing filter before the sampling we will end up with less distortion than if we just do the sampling right away.
True
Fourier transform can be thought of as the limit of the Fourier series as the period approaches infinity.
True
Ideal Sampling happens when we multiply the time domain signal x(t) with a pulse train with period Ts.
True
If we use an anti-aliasing filter before the sampling there will be no aliasing
True
If 𝑥(𝑡) is bandlimited to 𝐵 Hz then 𝑥(𝑡) can be perfectly recovered from it's samples provided that T𝑠 < 0.5/𝐵.
True
If 𝑥(𝑡) is bandlimited to 𝐵 Hz then 𝑥(𝑡) can be perfectly recovered from it's samples provided that 𝑓𝑠 >2𝐵.
True
In practice, no signal is ever absolutely bandlimited
True
In signal reconstruction, aliasing refers to reconstructing the wrong signal because of undersampling
True
Parseval's theorem for the Fourier series stated that the average power of a signal x(t) can be computed in either the time or frequency domains.
True
Sampling is the process by which a signal is converted from continuous time to discrete time.
True
The Fourier series represents a periodic function as a (possibly infinite) linear combination of complex sinusoids.
True
The Nyquist rate for sampling this signal 3cos(2𝜋𝑡)+2sin(3𝜋𝑡) should be 3 Hz
True
A function cannot be both time limited and bandlimited.
True
An anti-aliasing filter is an analog filter
True
For Fourier Series of a real-valued signal x(t), the DC power is |a0|2
True
For Fourier Series of a real-valued signal x(t), the power of the 1st harmonic is 2|a1|2
True
For Fourier Series, if x(t) is real and even, the Fourier Series coefficients (ak) will have a real value.
True
For Fourier Series, if x(t) is real-valued, the following conjugate symmetry relation is applicable : a−k = ak∗
True
For Fourier Series, if x(t) is real-valued, then Fourier series coefficients will follow |a−k|= |ak|
True
For Fourier series, the terms in the summation for k = 1 and k = -1 are known as the fundamental frequency components or first harmonic components, and have the fundamental frequency ω0.
True
For a continuous and periodic time domain signal, the frequency domain should be_________
Aperiodic Periodic Discrete
