2 y t 1 cos 3 t 2 1 ej 3 t 2 1 2 e j 2 3 t 2 1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: oblem 2 The p eriodic triangular wave shown below has Fourier series coefficients a k . x(t) 1 ··· ··· −4 −2 0 2 4 t � ⎧2 sin(kω/2) e−jk�/2 , � j (kω )2 ak = ⎧1 �, 2 k=0 ≤ k = 0. Consider the LTI system with frequency response H (j� ) depicted below: H (j� ) A2 x(t) H (j� ) y (t) A1 A3 −�3 −�2 −�1 �1 �2 �3 � Determine values of A1 , A2 , A3 , �1 , �2 , and �3 of the LTI filter H (j� ) such that � � 3ω y (t) = 1 − cos t. 2 At the b eginning, it is worth noting that the output y (t) contains only a DC component and � a single sinusoid with a frequency of 32 . H (j� ) is a linear system so the output will only have frequency components that exit in the input. Knowing that the input x(t) has a DC component and a fundamental frequency of �0 = � , let’s dissect y (t) into a DC component 2 5 and complex exponentials with a fundamental frequency of �0 = � . 2 y (t) = 1 − cos � 3ω t 2 � =1− ej 3� t 2 1 − 2 e −j 2 3� t 2 1 j (3) � t 1 j (−3) � t 2 e 2− e 2 2...
View Full Document

This document was uploaded on 02/09/2014.

Ask a homework question - tutors are online