![PROBLEM 2 150 pts.] A signal is consist of three sine functions: the first one, , has a wave frequency of 50 Hz, the second one, 2, has 100 Hz, and the last one, r3, has 200 Hz. However, each function has different amplitude: the amplitude of the first signal component x! is 10 cm, the amplitude of the second signal component xi s 5 cm; and the amplitude of the last signal component t3 is 1 cm. As a result, the signal can be expressed as f(t) 10-sin(2n . 50 . t) + 5 . Sin(2n . 100 . t) + 1 . sin(2π . 200 . t) The sampling frequency for this signal is 1000 Hz. The time vector for this signal ranges from 0 sec to 1 sec. 1) What is the minimum requirement for the sampling frequency? (Which value of the sampling frequency is needed to meet at least?). 2) As stated before, in this problem, the sampling frequency is prespecified as 1000 Hz. In this case, is aliasing expected to happen or not? why? 3) Plot the signal f(t). 4) plot the single-sided amplitude spectrum for this signal.](http://img.homeworklib.com/questions/1bc3cd70-01e3-11ec-9b59-6da76d841566.png?x-oss-process=image/resize,w_560)
Homework Answers
1) The minimum requirement for sampling frequency is that it should be greater than or equal to twice that of the maximum frequency of the signal. In this case, maximum frequency is 200 hz. Therefore, minimum required sampling frequency is 2 *200 = 400 hz.
2) Given, sampling frequency is 1000 hz. Since 1000 > 400 hz, so aliasing wont happen.
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PROBLEM 2 150 pts.] A signal is consist of three sine functions: the first one, ,...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoi...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling intervals: [30 points] • Ts= 0.5 sec. • Ts= 0.75 sec • Ts =1 sec. (a) For each case, also sketch the reconstructed continuous time signal from the samples using linear interpolation (i.e. connecting samples by straight lines). (b) In which case the sampled signal has aliasing distortion? What is the minimal sampling frequency and the corresponding sampling interval needed to avoid aliasing? 3....
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal ; c. Determine the frequency/frequencies of aliasing noise . Q2)...
Generate plots for the function in Example 8.1 with sample intervals of 0.5 sec, 1 sec, and 10 se...
Generate plots for the function in Example 8.1 with sample intervals of 0.5 sec, 1 sec, and 10 sec. Explain the results in light of the sampling theorem. Example 8.1 Sampling Theorem and Aliasing Consider the function FO sin( at)+sin br) Using a trigonometric identity for the sum of two sinusoidal functions, we can rewrite FO as the following product: a+ b If frequencies a and b are close in value, the bracketed term has a very low frequency in...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero ou...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
Modify the windowfft.m program used in the previous experiment, so x is the product of two...
Modify the windowfft.m program used in the previous experiment, so x is the product of two sinusoids x1 and x2. Let the modulating signal, x1, have a frequency of 1k Hz with amplitude of 1. Let the carrier signal, x2, have a frequency of 20k Hz with amplitude of 1. The Matlab code would look as follows % this is referred to as the modulating or message signal xl - sin(2*pi*f0*t) x2- sin(2 pi 20 O): % this is referred...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
Data communication Qs A signal has a bandwidth frequency of 150 Hz and the highest frequency...
Data communication Qs
A signal has a bandwidth frequency of 150 Hz and the highest frequency is 170 Hz. What is the lowest frequency of the signal? (just put the whole number. No decimal values. No units next to the number) A periodic signal completes one cycle in 0.04 second. What is the frequency? A sine wave completes 7200 cycles in one hour. What are its frequency and period? I: 50 Hz, II: 10 Hz, 0.1 seconds I: 25 Hz,...
Document a complete and thorough answer to Class Discussion Item 8.2 Class Discussion Item 8.2 Sa...
Document a complete and thorough answer to Class Discussion Item 8.2 Class Discussion Item 8.2 Sampling a Beat Signal What is the minimum sampling rate required to adequately represent the signal in Example &1? Example 8.1 Sampling Theorem and Aliasing Consider the function Fn- sin( ar) + sin( bry Using a trigonometric identity for the sum of two sinusoidal functions, we can rewrite FO as the following product: If frequencies a and b are close in value, the bracketed term...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
Generate plots for the function in Example 8.1 with sample intervals of 0.5 sec, 1 sec, and 10 sec. Explain the results in light of the sampling theorem. Example 8.1 Sampling Theorem and Aliasing Consider the function FO sin( at)+sin br) Using a trigonometric identity for the sum of two sinusoidal functions, we can rewrite FO as the following product: a+ b If frequencies a and b are close in value, the bracketed term has a very low frequency in...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
Modify the windowfft.m program used in the previous experiment, so x is the product of two sinusoids x1 and x2. Let the modulating signal, x1, have a frequency of 1k Hz with amplitude of 1. Let the carrier signal, x2, have a frequency of 20k Hz with amplitude of 1. The Matlab code would look as follows % this is referred to as the modulating or message signal xl - sin(2*pi*f0*t) x2- sin(2 pi 20 O): % this is referred...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
Data communication Qs
A signal has a bandwidth frequency of 150 Hz and the highest frequency is 170 Hz. What is the lowest frequency of the signal? (just put the whole number. No decimal values. No units next to the number) A periodic signal completes one cycle in 0.04 second. What is the frequency? A sine wave completes 7200 cycles in one hour. What are its frequency and period? I: 50 Hz, II: 10 Hz, 0.1 seconds I: 25 Hz,...
Document a complete and thorough answer to Class Discussion Item 8.2 Class Discussion Item 8.2 Sampling a Beat Signal What is the minimum sampling rate required to adequately represent the signal in Example &1? Example 8.1 Sampling Theorem and Aliasing Consider the function Fn- sin( ar) + sin( bry Using a trigonometric identity for the sum of two sinusoidal functions, we can rewrite FO as the following product: If frequencies a and b are close in value, the bracketed term...
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