(f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
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19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that ...
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...
(a) A system is generating the following continuous-time signal: x(t) = 1 + cos(100nt) + sin(300nt)...
(a) A system is generating the following continuous-time signal: x(t) = 1 + cos(100nt) + sin(300nt) An engineer wants to sample this signal to be analysed digitally on a computer. He decides to sample it at 500Hz. Did the engineer make the right decision? State why? What is its corresponding discrete-time signal x[n].
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist...
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first sampled at the rate of 80 samples per second and the result was processed with an ideal reconstruction filter, again assuming that sampling rate was 80 samples per second. What is the signal that results after the reconstruction? Show enough details in your answer to demonstrate that you understand the theory of sampling and reconstruction from samples. Hint: Write (t) as a sum of...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquis...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquist rate to get the sequence r[n]. (a) Sketch X(e) (b) If y[n] = [4n]. Sketch Y(e'"). (c) Is there any aliasing in the Fourier spectrum of yin]? Why or Why Not? (d) If z [n] = x-1, ketch the DTFT of z[n] (e) Is there any aliasing in the Fourier spectrum of [n]? Why or Why Not?
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is...
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs =...
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs = 8000 Hz and produces at its output a sampled discrete-time signal x$(t) = x(nTs), where To = 1/fs is the sampling period. If the sampled signal is passed through a unity-gain lowpass filter with cutoff frequency of fs/2, sketch the magnitude spectrum of the resulting signal for the following input signals: (a) x(t) = cos(6000nt). (b) x(t) = cos(12000nt). (c) x(t) = cos(18000nt).
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume...
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time...
Ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is s...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
please can discuss how you solve it For a continuous-time band-limited signal, x(t) = cos (4000nt)...
please can discuss how you solve it
For a continuous-time band-limited signal, x(t) = cos (4000nt) compute Nyquist sampling rate, 125. Also compute first 10 samples of the sampled signal, x (nts), for n > 0, that is, n 0 1 2 3 4 5 6 7 8 9 x(nts) Re-compute first 10 samples of the sampled signal, x(nts), for n > 0, that is, 0 2 3 4 8 9 x(nts) n 1 5 6 7 if x(t) is...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting sampl...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
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...
(a) A system is generating the following continuous-time signal: x(t) = 1 + cos(100nt) + sin(300nt) An engineer wants to sample this signal to be analysed digitally on a computer. He decides to sample it at 500Hz. Did the engineer make the right decision? State why? What is its corresponding discrete-time signal x[n].
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
1. Consider a signal of the form (t) = 2 cos(100nt) cos(1507) This signal is first sampled at the rate of 80 samples per second and the result was processed with an ideal reconstruction filter, again assuming that sampling rate was 80 samples per second. What is the signal that results after the reconstruction? Show enough details in your answer to demonstrate that you understand the theory of sampling and reconstruction from samples. Hint: Write (t) as a sum of...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquist rate to get the sequence r[n]. (a) Sketch X(e) (b) If y[n] = [4n]. Sketch Y(e'"). (c) Is there any aliasing in the Fourier spectrum of yin]? Why or Why Not? (d) If z [n] = x-1, ketch the DTFT of z[n] (e) Is there any aliasing in the Fourier spectrum of [n]? Why or Why Not?
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is...
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs = 8000 Hz and produces at its output a sampled discrete-time signal x$(t) = x(nTs), where To = 1/fs is the sampling period. If the sampled signal is passed through a unity-gain lowpass filter with cutoff frequency of fs/2, sketch the magnitude spectrum of the resulting signal for the following input signals: (a) x(t) = cos(6000nt). (b) x(t) = cos(12000nt). (c) x(t) = cos(18000nt).
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
please can discuss how you solve it
For a continuous-time band-limited signal, x(t) = cos (4000nt) compute Nyquist sampling rate, 125. Also compute first 10 samples of the sampled signal, x (nts), for n > 0, that is, n 0 1 2 3 4 5 6 7 8 9 x(nts) Re-compute first 10 samples of the sampled signal, x(nts), for n > 0, that is, 0 2 3 4 8 9 x(nts) n 1 5 6 7 if x(t) is...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
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