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Class%238-HOMEWORK

# Class%238-HOMEWORK - 5 Find Z transforms of x(n h(n and...

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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.
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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. )...
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