W17.4 We are given a periodic function f with period 2m and such that f(x) = -f(-x+a)for all æ.(a) Convince yourself that the condition f(x) = -f(-x + a) means that the graph of fis symmetric with respect to the point (5,0). In other words, check that the functiong(x) := f(x+ }) is odd.(b) Show that the Fourier coefficients ao, a2, a4, . .. of f are all 0.(c) Which other Fourier coefficients of f are 0?

We are given a periodic function f with period 2π and such that f(x)=-f(-x+π) for all x. a) We need…

W17.4 We are given a periodic function f with period 2a and such that f(x) = -f(-x+n) for all r. (a) Convince yourself that the condition f (x) = -f(-x + «) means that the graph of f is symmetric with respect to the point (,0). In other words, check that the function g(x) := f(x + }) is odd. (b) Show that the Fourier coefficients ao, a2, a4, . .. of f are all 0. (c) Which other Fourier coefficients of f are 0?

W17.4 We are given a periodic function f with period 2a and such that f(x) = -f(-x+n) for all r. (a) Convince yourself that the condition f (x) = -f(-x + «) means that the graph of f is symmetric with respect to the point (,0). In other words, check that the function g(x) := f(x + }) is odd. (b) Show that the Fourier coefficients ao, a2, a4, . .. of f are all 0. (c) Which other Fourier coefficients of f are 0?

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

8. For a positive, even and periodic function, what will be the integral of the function from -infinity to +infinity equal to? a) Non-zero Finite b) Zero c) Infinite d) None of the mentioned 178% (aseo aall ) ula Start W EN TOSHIBA INS 100LSCR DEL 144 ESC 40 BACK SPACE %23 %24 & 5 7 V 8. 94 FEX KRF %S4
A continuous time signal x is shown below x(t) 2 t 1 2 3 If periodic (t) = (t - 3m) then which of the following statements is true? Select one: O a. O b. O c. O d. periodic is periodic with fundamental period two. periodic has duration two and is periodic with fundamental period three. periodic is not periodic. periodic has duration three.
Plot the signal a(t) = 2, 9sin (2n3t) x [u(t - 1) – u(t - 3)]. IMPORTANT: To accurate drawing, find value of the sine function at t=1. Pay attention to the frequency of the signal when drawing. Write values of amplitude and time axis. Sloppy drawings are invalid.
Consider the following system. x[n] - oblem 70 Plot the output y[n] for n = -2,..., 2 when the input x[n] is the periodic input shown below. x[n] 1 1 P -2- -1-1 I 1 O -1/₂ D 2 -1-1 1 4 -1 y [n] n 9m
Electrical Engineering p x(t) 1 1 3 Consider the above figure which shows one period of the periodic signal r(t). Draw the magnitude and phase spectrum of x(t) for all frequencies between -0.5 Hz and 0.5 Hz. Also, write an approximation for r(t) as a sum of cosine functions for frequencies up to 0.5 Hz. Note that you do not need to write a closed form infinite sum.
7576 A time domain representation of a signal generally expresses how a signal changes with respect to time. True False "To perform phasor division of two phasors, its better expressed the phasors in polar form and then get the sum of all the individual magnitudes (amplitudes) and get the sum of all the individual arguments (phase angles)." O True False
17. The complex conjugate, or simply conjugate of a complex number is found by reversing the algebraic sign of the complex number's real and imaginary number. True False 18. Phase-factor measurement is the measurement of the time delay between four periodic signals. True False 22. All complex numbers are phasors but not all phasors are complex numbers. True False
Q1:- Find the power of the periodic signal f(t)/ volt 1 t/ sec 10 6 -1
topic:Fourier transform A option is correct
Q2/ Skitch the following aperiodic waveform in the time domain and calculate it is Fourier transform. - 22t3 2 %3D otherwise %3D
Sketch f(x) for several periods. If f(x) is a periodic function with period 2π where the value of f(x) in the interval -π
a) Figure 4 below shows a rectangular pulse. i. Derive the Fourier transform for x(t) using integration. ii. Sketch X(@). Label all the important information on the sketching. i. Predict what happens to the DC level as the pulse gets broader while the peak amplitude is maintained at A. x(t) A Activate Window t T T Go to Settings to activ Figure 4 Windows.