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1. Use the definition of the Continuous Time Fourier Transform (CTFT) X(f) of a signal x(t)...
Hello, I'm taking signal systems course. please solve this question in matlab as soon as possbile please. Question 1 a) Write a function that calculates the Continuous Time Fourier Transform o...
Hello, I'm taking signal systems course. please solve this
question in matlab as soon as possbile please.
Question 1 a) Write a function that calculates the Continuous Time Fourier Transform of a periodic signal x() Syntax: [w, X] = CTFT(t, x) The outputs to the function are: w = the frequencies in rad/s, and X = the continuous Fourier transform of the signal The inputs to the function are: x-one period of the signal x(t), andt the time vector The...
# 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...
(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...
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]...
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...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered?
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....
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).
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier...
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
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and prope...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t)
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,00...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
Hello, I'm taking signal systems course. please solve this
question in matlab as soon as possbile please.
Question 1 a) Write a function that calculates the Continuous Time Fourier Transform of a periodic signal x() Syntax: [w, X] = CTFT(t, x) The outputs to the function are: w = the frequencies in rad/s, and X = the continuous Fourier transform of the signal The inputs to the function are: x-one period of the signal x(t), andt the time vector The...
# 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...
(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...
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]...
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...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered?
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....
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).
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
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t)
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
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