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Homework Answers
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3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at...
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).
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)...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
A signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be ab...
A signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be able to reconstruct f(t) from these samples. If the sampled signal is passed through an ideal lowpass filter of bandwidth 100 Hz and unit gain, find the filter output. What is the filter output if its bandwidth is B Hz, where...
2.5. Given an analog signal x(t)5cos(2T 2, 5001) + 2cos(2T 4, 5001), for t2 0 sampled...
2.5. Given an analog signal x(t)5cos(2T 2, 5001) + 2cos(2T 4, 5001), for t2 0 sampled at a rate of 8,000 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 frequneuencis f aliasing noise.
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. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? ...
3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with...
The signal x(t)=cos(2πt) is ideally sampled with a train of impulses
The signal x(t)=cos(2πt) is ideally sampled with a train of impulses. Sketch the spectrum Xδ(f) of the sampled signal, and find the reconstructed signal x(t), for the following values of sampling period Ts and ideal lowpass reconstruction filter bandwidth W': (a) Ts = 1/4, W' = 2 (b) Ts= 1, W' = 5/2(c) Ts = 2/3, W' = 2
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with...
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with cutoff frequency wc = 10007. If impulse-train sampling is performed on x(t), which of the following sampling periods would guarantee that y(t) can be recovered from its sampled version using an appropriate lowpass filter? (a) T=0.5x10-3 (b) T=2x10-3 (c) T=10-4
# 1 : Imagine that you have a continuous-time signal x(t) whose continuous-time Fourier transform is...
# 1 : Imagine that you have a continuous-time signal x(t) whose continuous-time Fourier transform is as given below -25 -20 f, Hz -10 10 20 25 (a) (10 pts) Imagine that this signal is sampled at the sampling rate of F, 65 Hz. Sketch the FT of the resulting signal that would be at the output of an ideal DAC (like we discussed in class) when given these samples. (b) (10 pts) Repeat part (a) for the case that...
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).
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
A signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be able to reconstruct f(t) from these samples. If the sampled signal is passed through an ideal lowpass filter of bandwidth 100 Hz and unit gain, find the filter output. What is the filter output if its bandwidth is B Hz, where...
2.5. Given an analog signal x(t)5cos(2T 2, 5001) + 2cos(2T 4, 5001), for t2 0 sampled at a rate of 8,000 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 frequneuencis f aliasing noise.
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. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with...
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with cutoff frequency wc = 10007. If impulse-train sampling is performed on x(t), which of the following sampling periods would guarantee that y(t) can be recovered from its sampled version using an appropriate lowpass filter? (a) T=0.5x10-3 (b) T=2x10-3 (c) T=10-4
# 1 : Imagine that you have a continuous-time signal x(t) whose continuous-time Fourier transform is as given below -25 -20 f, Hz -10 10 20 25 (a) (10 pts) Imagine that this signal is sampled at the sampling rate of F, 65 Hz. Sketch the FT of the resulting signal that would be at the output of an ideal DAC (like we discussed in class) when given these samples. (b) (10 pts) Repeat part (a) for the case that...
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