Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part35

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part35

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 7 53 Copyright © Orchard Publications Exercises 7.16 Exercises 1 . Compute the first 5 components of the trigonometric Fourier series for the waveform shown below. Assume . 2 . Compute the first 5 components of the trigonometric Fourier series for the waveform shown below. Assume . 3 . Compute the first 5 components of the exponential Fourier series for the waveform shown below. Assume . 4 .Compute the first 5 components of the exponential Fourier series for the waveform shown below. Assume . ω 1 = 0 ω t A ft () ω 1 = 0 ω t A ω 1 = 0 ω t A ω 1 = 0 ω t A2 A 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 7 Fourier Series 7 54 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications 5 . Compute the first 5 components of the exponential Fourier series for the waveform shown below. Assume . 6. Compute the first 5 components of the exponential Fourier series for the waveform shown below. Assume . ω 1 = 0 ω t A ft () ω 1 = 0 ω t A A
Background image of page 2
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 7 55 Copyright © Orchard Publications Solutions to End of Chapter Exercises 7.17 Solutions to End of Chapter Exercises 1 . This is an even function; therefore, the series consists of cosine terms only. There is no half wave symmetry and the average ( component) is not zero. We will integrate from to and multiply by . Then, (1) From tables of integrals, and thus (1) becomes and since for all integer , (2) We cannot evaluate the average from (2); we must use (1). Then, for , or We observe from (2) that for , . Then, 0 ω t A ft () A π ---t 2 π π π 2 π DC 0 π 2 a n 2 π -- A π --- tn t cos t d 0 π 2A π 2 ------- t cos t d 0 π == xa x cos x d 1 a 2 ---- ax cos x a a sin x + = a n π 2 1 n 2 nt cos t n sin +   0 π π 2 1 n 2 n π cos t n π 1 n 2 0 sin + π sin 0 = n a n π 2 1 n 2 n π cos 1 n 2 n 2 π 2 ---------- n π 1 cos 12 a 0 n0 = 1 2 --a 0 2 π 2 -------- tt d 0 π A π 2 ----- t 2 2 0 π A π 2 π 2 2 = a 0 A2 = ne v e n = a v
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

Page1 / 8

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part35

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online