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. For the same signal in question 1, s(t) = c
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Plot the signal s(t) = cos(2πt), and then illustrate the
resulting samples with the following sampling...
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
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...
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...
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Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
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).
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Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
number 2 ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z()...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
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...
1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume...
1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume any arbitrary spectrum for this signal. (Note that this signals also has frequencies from 0 to \(-10 \mathrm{KHz} .)\) a) Draw the frequency spectrum of the signal after it has been sampled with a sampling frequency \(\mathrm{F}_{\mathrm{s}}=25 \mathrm{kHz}\) b) What range of sampling frequencies allows exact reconstruction of this signal from its samples? c) How is the original signal reconstructed from the sampled signal?...
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,...
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...
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...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
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).
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
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...
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,...
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