Class%238-HOMEWORK

Class%238-HOMEWORK - 5. Find Z transforms of x(n) , h(n),...

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

View Full Document Right Arrow Icon
ECE155A Fall 07 Lecturer – Dr. Vlad Dorfman Class #8 Equalization - Homework Due Oct 29, 2007, 10 points each 1. Find Z-transform and DTFT of a m u ( n ) , | a | < 1, u ( n ) is a step function , u ( n ) =0 for n<0 and u ( n )=1 for n>1. 2. Derive the formula for the sum of geometric progression 1+q+q 2 +q 3 +… where q is a real number, |q|<1 3. Let h(n) be a discrete channel response with h(0)=1, h(1)=-q, and h(n)=0 for n<0 and n > 1. Let x(n) be an input to the discrete channel h(n), x(n)=q n , n 0, x(n)=0 for n<0, where q is a real number, |q|<1 . Channel h and input x could be also described as h(n)=[1,-q] and x(n)=[1,q,q 2 ,q 3 ,q 4 ,…] where [. .] means a sequence of numbers. Find the output of the channel. 4. Let channel h and input x could be also described h(n)=[1,q,q 2 ,q 3 ,q 4 ,…] as x(n)=[1,-q] and. Find the output of the channel.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5. Find Z transforms of x(n) , h(n), and channel output y(n) in problems 3 and 4. Explain the results of 3 and 4 in terms of the formula Y(z)=H(z)X(z) . 6. Let sig1 = [1 2 3 4 5] and sig2 = [1 1]. Let s_out be the convolution of sig1 and sig2. Let H1(w), H2(w), and Hout(w) be frequency responses of sig1,2, and _out respectively. Use Matlab to compare graphically the spectrum magnitude |H1(w)*H2(2)| and |Hout(w)|. (||means absolute value, i.e. magnitude only, no phase) . Since the two magnitudes are expected to be equal, use different line patterns to plot those. (Hint - use 'freqz' to find H(w). If you have no Signal Processing toolbox, make your own routine by using DTFT definition. The latter is shown in the lectures' presentation. )...
View Full Document

This note was uploaded on 11/11/2009 for the course ECE 670377 taught by Professor Wolf during the Winter '07 term at UCSD.

Ask a homework question - tutors are online