Consider the following continuous-time signal.
x(t) = 1 for m < t < m + 1
−1 for m + 1 < t < m + 2
for m = − 4,−2, 0, 2, 4, · · ·
Sketch the following signals.
(a) x(t)
(b) y(t) = 2x(2t − 1) + 1
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Consider the following continuous-time signal. x(t) = 1 for m < t < m + 1...
Question #5: Consider the continuous-time signal shown below. x(t) -6 -4 -2 4 -2 (a) Sketch y(t) x1) (b) Sketch y(t) 2x[t- 2) (c) Sketch y(t) - 5x(t/3) (d) Sketch y(t) x(t) -x(-t)
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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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(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2 x 103Joules). The signal ra(t) is sampled at a rate of 500 samples/sec to yield its discrete-time counter part (n) (a) Find ti, and hence sketch ra(t). (b) From part (a), plot r(n) and finds its energy (c) Derive an expression for the Fourier transform of a(n), namely X(ew). (d) Plot the magnitude spectrum (1X(e)) and phase spectrum 2(X(e). (e) Consider the signal y(n)...
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier transform: X(jw) = J 1 - if we l-207, 207] if|wl > 207 (3) Let y(t) = x(26) cos? (507). Sketch Y (w), i.e., the Fourier transform of y(t). (Note that 2 1 + cos(20) cos? (0) = 2
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answer a and b only Suppose that two continuous time signal are given by x(t) and v(t) as: x(t) = u(t) - 2u(t - 1) + u(t - 2) v(t) = u(t)- uſt - 1) Answer the following questions: (a) Plot signals x(t) and v(t). (b) Find the convolution of y(t) = x(t-3) = v(t) (c) Plot for y(t).