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4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum...
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth...
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth of the message signal. For the three message signals below determine the Nyquist rate and the Nyquist interval for each. a) m(t) = 0.5 cos(150 ) + sin(300Ft) + 0.75 cos(350ft) b) m(t) = 2 cos(120rt) sin(3007) c) m(t) = sinc(4000) = sin(400m) Recall: the Fourier transform of a sinc waveform is a rectangular pulse
(a) Sketch the spectrum of the signal r(t). Show the spectrum as a function of f...
(a) Sketch the spectrum of the signal r(t). Show the spectrum as a function of f in Hz For the rest of this problem, assume that the signal is sampled at a rate of fs 50 Hz. (b) Sketch the spectrum for the sampled signal rn). Your spectrum should be shown as a function of the normalized frequency over the interval-2π < -+2T. c) Write an equation for the sampled signal [n. (d) Suppose that the signal is reconstructed from...
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) 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...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for sampling. Consider a signal x,(t) = cos(40t) cos(80t). Sketch the 2-sided complex spectrum and [5 pts] determine the minimum sampling rate that can be used to sample the signal without causing aliasing. [5 pts] Repeat Part a for the signal x2 t) cos(4 x 103t) sin(3 x 103Tt) cos(8 x 10Tt). [5 pts] Repeat Part a for the signal x3(t) cos(4 x 103Trt) sin(3...
Find the Nyquist rates for these signals: (a) X(t) = sinc (20) (b)x(t) = 4 sinca...
Find the Nyquist rates for these signals: (a) X(t) = sinc (20) (b)x(t) = 4 sinca (100t) (C) x(t) = 8 sin(50TTT) (d) x(t) = 4 sin(30TTt) + 3 cos(70nt) (e) X(t) = rect(300t) (f) X(t) = -10 sin(40nt) cos(300Tt) (g) X(t) = sinc(t/2)*710(t) (h) x(t) = sinc(t/2) 70.1() (i) X(t) = 8tri((t - 4)/12) (1) X(t) = 13e-201 cos(70TTt)u(t) (k) x(t) = u(t)-u(t-5)
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...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each sign...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
Sketch the frequency spectrum of he following signal and indicate the complex magnitude of each. All...
Sketch the frequency spectrum of he following signal and
indicate the complex magnitude of each. All amplitudes must be
positive
Determine fundamental frequency and period
*all phases need to be written in terms of pi between
-pi and pi.
Sketch the frequency spectrum of the following signal and indicate the complex magnitude of each frequency component Manipulate phase as necessary to plot all components of the spectrum with positive amplitudes: x(t) = 14 cos( 1 60mt-π/4) + 5 cos(280mt-2π/3) -cos(600πt...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that ...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (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)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth of the message signal. For the three message signals below determine the Nyquist rate and the Nyquist interval for each. a) m(t) = 0.5 cos(150 ) + sin(300Ft) + 0.75 cos(350ft) b) m(t) = 2 cos(120rt) sin(3007) c) m(t) = sinc(4000) = sin(400m) Recall: the Fourier transform of a sinc waveform is a rectangular pulse
(a) Sketch the spectrum of the signal r(t). Show the spectrum as a function of f in Hz For the rest of this problem, assume that the signal is sampled at a rate of fs 50 Hz. (b) Sketch the spectrum for the sampled signal rn). Your spectrum should be shown as a function of the normalized frequency over the interval-2π < -+2T. c) Write an equation for the sampled signal [n. (d) Suppose that the signal is reconstructed from...
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) 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...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for sampling. Consider a signal x,(t) = cos(40t) cos(80t). Sketch the 2-sided complex spectrum and [5 pts] determine the minimum sampling rate that can be used to sample the signal without causing aliasing. [5 pts] Repeat Part a for the signal x2 t) cos(4 x 103t) sin(3 x 103Tt) cos(8 x 10Tt). [5 pts] Repeat Part a for the signal x3(t) cos(4 x 103Trt) sin(3...
Find the Nyquist rates for these signals: (a) X(t) = sinc (20) (b)x(t) = 4 sinca (100t) (C) x(t) = 8 sin(50TTT) (d) x(t) = 4 sin(30TTt) + 3 cos(70nt) (e) X(t) = rect(300t) (f) X(t) = -10 sin(40nt) cos(300Tt) (g) X(t) = sinc(t/2)*710(t) (h) x(t) = sinc(t/2) 70.1() (i) X(t) = 8tri((t - 4)/12) (1) X(t) = 13e-201 cos(70TTt)u(t) (k) x(t) = u(t)-u(t-5)
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...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
Sketch the frequency spectrum of he following signal and
indicate the complex magnitude of each. All amplitudes must be
positive
Determine fundamental frequency and period
*all phases need to be written in terms of pi between
-pi and pi.
Sketch the frequency spectrum of the following signal and indicate the complex magnitude of each frequency component Manipulate phase as necessary to plot all components of the spectrum with positive amplitudes: x(t) = 14 cos( 1 60mt-π/4) + 5 cos(280mt-2π/3) -cos(600πt...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (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)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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