3.6. Consider three continuous-time periodic signals whose Fourier series repres= tions are as follows: 100 \k X1(t) = k 0 100 x2(t) = cos(km)eik, k=-100 ebonaoqe ts100 x3(1) = j sin (km leik. 2 k=-100 Use Fourier series properties to help answer the following questions: (a) Which of the three signals is/are real valued? (b) Which of the three signals is/are even?

3.6. Consider three continuous-time periodic signals whose Fourier series repres= tions are as follows: 100 \k X1(t) = k 0 100 x2(t) = cos(km)eik, k=-100 ebonaoqe ts100 x3(1) = j sin (km leik. 2 k=-100 Use Fourier series properties to help answer the following questions: (a) Which of the three signals is/are real valued? (b) Which of the three signals is/are even?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Consider the following discrete time signal periodic with N?[?]=1+sin(2??)?+3cos(2??)?+cos(4???+?2)Find the Fourier series representation of ?[?], i.e. find the Fourier series coefficients ?0, ?−1, ?1, ?−2 and ?2.
a. Show that 2-D discrete Fourier Transform of a M × N digital image is periodic.That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center ofthe 2-D array of frequency plane.
Find the Fourier coefficients c0, c1, c2, c3 for the discrete time signal given as x [n] = [4,5,2,1]. and plot the amplitude and power density spectra for the sign x [n].
The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as ck=(c-8,c-7,c-6,6-j,c-4,c-3,-5,c-1,c0,c1,-5,6-j) .Find the missing coefficients and plot its magnitude spectrum for -8≤k≤3.
Consider two discrete signals x1[k] and x2[k]. Let x1[k]; x2[k] be periodic signals with periods N,M respectively. Define y[k] = x1[k] + x2[k]. a) Show that y[k] is periodic with N M. b) Let Fourier coefficients of x1[k] and x2[k] be ak, bk respectively. Find Fourier coefficients ck of y[k] in terms of ak and bk.
A power signal depending on time t is written P (t) = P0cos (ωt) cos (ωt), with P0 in watts (W) and t in s (seconds). What are the amplitudes of the non-zero harmonics in the real Fourier spectrum of this signal (i.e. corresponding to the amplitudes an and bn)?Please choose at least one answer:.
A. Consider the two signals whose Fourier Series Spectrum as shown below. Assume that the units of frequency are kiloHertz (kHz). Look at the figure in the picture. What is the Fourier Series Spectrum of the product of these two signals? Pick among the choices. ============================================ B. Suppose that a signal cos⁡(2π⋅10t) modulates a cosinusoidal carrier cos⁡(2π⋅250t), and then mixed with another cosine at the same frequency, i.e. y(t)=cos⁡(2π⋅10t)⋅cos⁡(2π⋅250t)⋅cos⁡(2π⋅250t) Which of the following is an equivalent expression for y(t)? Select one: a. cos⁡(2π⋅510t) b. 0.5cos⁡(2π⋅240t)+0.5cos⁡(2π⋅260t) c. 0.5cos⁡(2π⋅250t)+0.25cos⁡(2π⋅240t)+0.25cos⁡(2π⋅260t) d. 0.5cos⁡(2π⋅10t)+0.25cos⁡(2π⋅490t)+0.25cos⁡(2π⋅510t)
An analog signal xa(t) has a continuous fourier transform that follows the attached image. If the signal is sampled at 600 samples/sec, the DTFT is the second image. What's the sketch of the spectrum Xa(F) of the origial analog signal?
a. Which of the following is true? The Fourier transform of a unit rectangular pulse is A. real. B. not oscillating. C. complex. D. neither real nor complex. b. Which of the following is true? For system and signal operations, the symbol “*” is typically shared between A. convolution and complex conjugate. B. linear combination and complex conjugate. C. orthogonality and complex conjugate. D. multiplication and complex conjugate. c. Which of the following is true? The Fourier transform is based on A. The Fourier series by substituting the signal x(t) into Fourier coefficient’s expression. B. The Fourier series by substituting the Fourier coefficient’s expression into a random signal which is periodic over a defined period. C. The Fourier series by substituting the Fourier coefficient’s expression into x(t). D. The Fourier series because this is a logical process.
a) Make a plot of the normalized fft magnitude as a function of frequency (real frequency in Hz). Only display the frequency range between -1kHz and 1kHz. b) On the same figure as part (c), superimpose the magnitude of the Fourier series coefficients, |??|, as a function of frequency as a stem plot. Again, only display the frequency range between -1kHz and 1kHz. How well do they compare? Hint*: Consider making a frequency vector containing only the Fourier harmonic frequencie
Answer the following four questions according to the following signal below: 1)the frequency of the signal? 2)the period of the signal? 3)frequencies exists in the frequency spectrum of signal? 4)expressions of the Fourier series expansion of this signal?
Obtain the Fourier Transform to the rectangular pulse of duration 2 second and having a magnitude of 10 volts.