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• ### The Fourier transform W(f) of a time domain signal w(t) is given by: W(f) = 5.87...

The Fourier transform W(f) of a time domain signal w(t) is given by: W(f) = 5.87 exp[ -( 0.047 f )2 ] Find the imaginary part of the Fourier transform of the shifted signal w(t - 0.50) at the frequency 3.24 Hz. The correct answer is 3.93

• ### Problem 5 (20 points) Find the time-domain signal corresponding to the Fourier transform X(jw) whose magnitude...

Problem 5 (20 points) Find the time-domain signal corresponding to the Fourier transform X(jw) whose magnitude and phase characteristics are shown in Figure P5. ZX(jw) .W o) -22 Figure P5

• ### QUESTION 1 Consider the time domain signal shown below. Determine the magnitude of the Fourier Tr...

QUESTION 1 Consider the time domain signal shown below. Determine the magnitude of the Fourier Transform, X(w), at a frequency of ω : 22 rad/sec, for a-3, b = 2, and c=2 be" for te[0,c] x(t)-| 0 forte(0,c] QUESTION 1 Consider the time domain signal shown below. Determine the magnitude of the Fourier Transform, X(w), at a frequency of ω : 22 rad/sec, for a-3, b = 2, and c=2 be" for te[0,c] x(t)-| 0 forte(0,c]

• ### Q.3) 120 Marks] [8 Marks] Determine the DTFT of the following DT signals i) x[n] =...

Q.3) 120 Marks] [8 Marks] Determine the DTFT of the following DT signals i) x[n] = (0.5)" [u[n]-n(n-3)) a) ii) ? [n] = n (0.5)" u[n-2] b) [8 Marks] Consider the following CTFT pair: jw x(t) ?? (-v^2 + 5 i) e -/00t x(t) 6) using the CTFT properties determine the Fourier transform (CTFT) of: i x(3t-6) e) [4 Marks] Prove the Parseval's relationship for a CT signal x e

• ### 1. Draw frequency domain representations (sketches of the real and imaginary parts of the Fourier transform)...

1. Draw frequency domain representations (sketches of the real and imaginary parts of the Fourier transform) for both cos(2*pi*fc*t) and sin(2*pi*fc*t), for a carrier waveform. ____________________ Now suppose we have a sinusoidal signal of frequency fi, where fi << fc. Let the signal be m(t)=cos(2*pi*fi*t) and the carrier be cos(2*pi*fc*t). Say we mix m(t) up to carrier frequency fc when we multiply m(t) by the carrier to create the modulated signal, s(t) = m(t) * cos(2*pi*fc*t). Draw the real part...

• ### A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform...

A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks] A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...

• ### 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...

• ### Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of t...

Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of the Fourier transform found in the "Properties of Fourier Transforms" table in textbook and the "Famous Fourier Transforms Table" in textbook instead of direct integration as much as possible to simplify your calculation wherever appropriate: 2-2

• ### (a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r?...

(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...

• ### This is in electrical engineering signals, I NEED IT ASAP PLEASE!! (b) A continuous-time LTT system...

This is in electrical engineering signals, I NEED IT ASAP PLEASE!! (b) A continuous-time LTT system has an input (t) and an output y(t). The frequency response of the system is (w). 0) (1 point) Write an equation that describes the relationship between the Fourier trans- forms of the input and output (X (jw) and Y Gw)) and the frequency response (jw). For the rest of the problem, assume that X(jw) and (w) are as shown in the plots below....