Enter the strength of the impulse of the third smallest positive frequency. Answer: Check
When the continuous time signal is reconstructed from its sa ples, the information n the interval
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Consider the continuous-time signalxt) 0.5 cos(2T 1000r). This is a tone with frequency 1000 Hz. ...
Frequency multiplication. Sample x(t) = cos 3πt at the rate of 4 Hz and send impulse...
Frequency multiplication. Sample x(t) = cos 3πt at the rate of 4 Hz and send impulse samples through an ideal low-pass filter with the cutoff frequency at fc and gain = 1/4. Find and plot the Fourier transform of the reconstructed signal z(t) and its time expression for fc = 2, 3, 4, 5, 6 Hz.
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of t...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
# 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...
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...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
4. (a) Consider a continuous-time signal given by j101 f(t)= e ' [u(t) - u(t –...
4. (a) Consider a continuous-time signal given by j101 f(t)= e ' [u(t) - u(t – 2)] (i) Find the Fourier transform of f(t) using the properties listed in the Appendix on page 6. (ii) If the signal f(t) is sampled in the time domain, what is the Nyquist rate (in Hertz) of f(t)? Comment on your result. (8 Marks)
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?
21 Consider a continuous-time signal ( of finite energy, with a continuous spectrum6(f). Assume that GU)...
21 Consider a continuous-time signal ( of finite energy, with a continuous spectrum6(f). Assume that GU) is sampled uniformly at the discrete frequencies f = k thereby obtaining the sequence of frequency samples G(kF), where k is an integer in the entire range -oo < k < o, and F, is the frequency sampling interval. Show that if g(t) is duration- limited, so that it is zero outside the interval -T < t < T, then the signal is completely...
Insted of the equation on the pic, use this equation please 5e^-4t 3r x(t)-10e' for t,t...
Insted of the equation on the pic, use this equation
please
5e^-4t
3r x(t)-10e' for t,t 20 Assume 0-0 for I<0. Sketch the signal showing the major points of interest a) Calculate the Continuous Time Fourier Transform of *C b) Calculate the total energy of ( c) Using Parseval's theorem, compute the energy spectral density, ESD of"C) d) Sketch the ESD of "showing the major features. e) Using the ESD obtained from c), now calculate the essential bandwidth B Hz...
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).
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
# 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...
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...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
4. (a) Consider a continuous-time signal given by j101 f(t)= e ' [u(t) - u(t – 2)] (i) Find the Fourier transform of f(t) using the properties listed in the Appendix on page 6. (ii) If the signal f(t) is sampled in the time domain, what is the Nyquist rate (in Hertz) of f(t)? Comment on your result. (8 Marks)
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?
21 Consider a continuous-time signal ( of finite energy, with a continuous spectrum6(f). Assume that GU) is sampled uniformly at the discrete frequencies f = k thereby obtaining the sequence of frequency samples G(kF), where k is an integer in the entire range -oo < k < o, and F, is the frequency sampling interval. Show that if g(t) is duration- limited, so that it is zero outside the interval -T < t < T, then the signal is completely...
Insted of the equation on the pic, use this equation
please
5e^-4t
3r x(t)-10e' for t,t 20 Assume 0-0 for I<0. Sketch the signal showing the major points of interest a) Calculate the Continuous Time Fourier Transform of *C b) Calculate the total energy of ( c) Using Parseval's theorem, compute the energy spectral density, ESD of"C) d) Sketch the ESD of "showing the major features. e) Using the ESD obtained from c), now calculate the essential bandwidth B Hz...
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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