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2) (35 points) Given the following continuous-time aperiodic signal. x(t) A t T 2 2 a....
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2...
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2 2 a. I (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20...
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
A) Assume that a continuous-time aperiodic signal x(t) is real. Prove that the spectrum X(jω) satisfies...
A) Assume that a continuous-time aperiodic signal x(t) is real. Prove that the spectrum X(jω) satisfies the following property: X(jω) =X(−jω)∗ where ∗ denotes conjugation. B) Assume that a continuous-time aperiodic signal x(t) is real and even. Prove that the spectrum X(jω) is real and even.
# 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...
(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2...
(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)...
(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...
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...
Now use MATLAB to generate and plot 15seconds of this signal in the time-domain.Use the fft()...
Now use MATLAB to generate and plot 15seconds of this signal
in the time-domain.Use the fft() function to find the fourier
transform of this signal and plot its magnitude spectrum
School of Engineering Task 3 - The Fourier Transform: Scaling property Exercise: Let's take a look now at using the Fourier transform on aperiodic signals. Consider the real exponential signal from the discharging capacitor in tas 3 of laboratory 1 which was found to be: You(t)=e"u(t) Begin by calculating manually...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f #...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
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) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2 2 a. I (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
# 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...
(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)...
(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...
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...
Now use MATLAB to generate and plot 15seconds of this signal
in the time-domain.Use the fft() function to find the fourier
transform of this signal and plot its magnitude spectrum
School of Engineering Task 3 - The Fourier Transform: Scaling property Exercise: Let's take a look now at using the Fourier transform on aperiodic signals. Consider the real exponential signal from the discharging capacitor in tas 3 of laboratory 1 which was found to be: You(t)=e"u(t) Begin by calculating manually...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
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]...
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