ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform.
(c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series representation by finding (1) the fundamental frequency wo (2) the DC value (3) the Fourier coefficients ak for kメ0.
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(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts)...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
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....
1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T...
1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T = 4 x 10-4. For each of the following sets of constraints on r(t) and/or X(ju), does the sampling theorem guarantee that r(t) can be recovered exactly from p(t)? a. X(ju) = 0 for l니 > 1000-r b, X(ju) = 0 for lal > 5000π c. R(X(ju))-0 for lwl > 1000-r d, x(t) real and X(jw)-0 for w > 1000π e. x(t) real and X(jw)-0...
Don't need to do #1. Please go into detail on how you solved #2 and #3 The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in th...
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc (t) 2/
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc...
Let X(w) denote the Fourier transform of the signal x(t) depicted in Figure P4.25. x (t)...
Let X(w) denote the Fourier transform of the signal x(t) depicted in Figure P4.25. x (t) 2 1 0 1 2 3 t Figure P4.25
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) =...
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) = 25 + (w- 1)225(w+1)2 (c) (4 pts) x(t) is given as x(t)-π inc(t) cos(nt). Find X(jw) (d) (4 pts) 2(t) is given as 2(t) e Áil+ 3) + e' ỗ(t-3). Find X (jw). Simplify the answer as (e) (4 pts) 2(t) is given as r(t) = rect(2(t )) reetgehj)). Hint: use Fourier Transform pair: sine(t)艹rect( ) much as possible Find X(jw). Simplify the answer...
how to derive the underlying signal x(t) using the definition of the Inverse Fourier transform Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the i...
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2....
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
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
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
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....
1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T = 4 x 10-4. For each of the following sets of constraints on r(t) and/or X(ju), does the sampling theorem guarantee that r(t) can be recovered exactly from p(t)? a. X(ju) = 0 for l니 > 1000-r b, X(ju) = 0 for lal > 5000π c. R(X(ju))-0 for lwl > 1000-r d, x(t) real and X(jw)-0 for w > 1000π e. x(t) real and X(jw)-0...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc (t) 2/
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc...
Let X(w) denote the Fourier transform of the signal x(t) depicted in Figure P4.25. x (t) 2 1 0 1 2 3 t Figure P4.25
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) = 25 + (w- 1)225(w+1)2 (c) (4 pts) x(t) is given as x(t)-π inc(t) cos(nt). Find X(jw) (d) (4 pts) 2(t) is given as 2(t) e Áil+ 3) + e' ỗ(t-3). Find X (jw). Simplify the answer as (e) (4 pts) 2(t) is given as r(t) = rect(2(t )) reetgehj)). Hint: use Fourier Transform pair: sine(t)艹rect( ) much as possible Find X(jw). Simplify the answer...
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
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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