07-Class.10.Problems - ECE155A – PROBLEMS Vlad Dorfman...

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Unformatted text preview: ECE155A – PROBLEMS Vlad Dorfman – Class #10 Due: 2/19/07 1. Noise Enhancement. Let s(t) be the Lorentzian step response of the channel ( s(t) = 1/(1+(2*t/PW50)^2) ), and suppose we design a zero-forcing linear equalizer with target z(t)=sinc(t/T). If sampled, z(kT) = δ (k) and therefore will have no ISI. The formula for the frequency response of the continuous zero-forcing equalizer is ⎪ ⎩ ⎪ ⎨ ⎧ ≤ = otherwise S T G T , ), ( ) ( π ω ω ω The frequency response of the Lorentzian is 2 50 50 2 ) ( ω π ω PW e PW S − = a. Plot G ( e j ω ), the frequency response of the equalizer for PW50=1 and D=PW50/T=1.0, 1.6, 2.0 ,and 2.5. Organize your M-files as a script, calling a function eq_fun(D,PW50). In your script file set PW50=1, then call eq_fun(D,PW50) with the requested values of D. (Comment: the problem shows what happens if different numbers of bits are placed into the constant area; this is represented by the PW50 value which is the same for all cases with only the density D changing). b. Calculate the noise power at the output of the equalizer for the above values of normalized density D . If you cannot find an analytical solution, you may use a computer to make an approximation, setting σ 2 = 1 in your eq_fun. Hint: For a linear system that has a FT magnitude |H( ω )|, and input random process X(t) with power spectral density S X ( ω ), the output power spectral density will be S Y ( ω ) = |H( ω )| 2 S X ( ω ). c. Make your conclusions as to dependency of noise enhancement on parameter D assuming the target z(t)=sinc(t/T). 2. Zero-Forcing Equalizer Implementation in Frequency Domain Consider a discrete-time channel impulse response h [ k ] defined as h (-2)=-2, h (-1)=-0.5, h (0)=5, h (1)=2, h (2)=1, h (k)=0 for |k| > 2. Use Matlab commands fft and ifft to determine (which is approximation, since fft...
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This note was uploaded on 11/11/2009 for the course ECE 670377 taught by Professor Wolf during the Winter '07 term at UCSD.

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07-Class.10.Problems - ECE155A – PROBLEMS Vlad Dorfman...

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