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Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier...
x(t) has the fourier transform x(jw) show dx(t)/dt has the fourier transform jw x(jw)
x(t) has the fourier transform x(jw) show dx(t)/dt has the fourier transform jw x(jw)
(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)...
(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) 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...
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform...
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform of the following signals in terms of X(jo) a. y(t)-etx(t 1) b. y(t)-x(-t) x(t-1) c. y(t)tx(t)
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...
Consider a signal x(t) = e-tu(t), and the signal y(t) below: dx(t) y(t) = 3e-33+ z(t...
Consider a signal x(t) = e-tu(t), and the signal y(t) below: dx(t) y(t) = 3e-33+ z(t – 5) + 5* dt Va) What is X(jw), the Fourier transform of æ(t)? b) Find the phase of the complex number X(j1). c) Find Y(jw), the Fourier transform of y(t). d) Find the magnitude of the complex number Y(j1).
(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...
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2...
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2 0 -1 -2 -3 5 4 3-2 0 2 3 4 5 a) b) Using known Fourier transforms for the terms of y(t), find Y(j). (Hint: you will have to apply some c) Apply differential properties to X(ju) to verify your answer for part b Differentiate x(t), y(t) = dx/dt. Note, the derivative should have a step function term. Include a sketch of y(t)...
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)...
Find the inverse Fourier transform for the following signals. X(e^jw) = 2 cos(w)
Find the inverse Fourier transform for the following signals. X(e^jw) = 2 cos(w)
(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) 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...
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform of the following signals in terms of X(jo) a. y(t)-etx(t 1) b. y(t)-x(-t) x(t-1) c. y(t)tx(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 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...
Consider a signal x(t) = e-tu(t), and the signal y(t) below: dx(t) y(t) = 3e-33+ z(t – 5) + 5* dt Va) What is X(jw), the Fourier transform of æ(t)? b) Find the phase of the complex number X(j1). c) Find Y(jw), the Fourier transform of y(t). d) Find the magnitude of the complex number Y(j1).
(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...
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2 0 -1 -2 -3 5 4 3-2 0 2 3 4 5 a) b) Using known Fourier transforms for the terms of y(t), find Y(j). (Hint: you will have to apply some c) Apply differential properties to X(ju) to verify your answer for part b Differentiate x(t), y(t) = dx/dt. Note, the derivative should have a step function term. Include a sketch of y(t)...
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)...
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