Q2) The result of a single pulse (impulse) transmission is a received sequence o
ID: 2266903 • Letter: Q
Question
Q2) The result of a single pulse (impulse) transmission is a received sequence of samples (impulse response), with values 0.1, 0.3,-0.2, 1.0, 0.4, -0.1, 0.1, where the leftmost sample is the earliest. The value 1.0 corresponds to the mainlobe of the pulse, and the other entries correspond to the adjacent samples. Design a 3-tap transversal equalizer that forces the ISI to be zero at one sampling point on each side of the mainlobe. Calculate the values of the equalized output samples at times . After equalization, whatis the largest magnitude sample contributing to ISI, and what is the sum of all the ISI magnitudes?Explanation / Answer
A sequence of samples (impulse response) which is given as :
0.1, 0.3, -0.2, 1.0, 0.4, -0.1, 0.1
where, leftmost sample is the earliest.
We know that, the value 1.0 corresponds to the mainlobe of a pulseand the other entries correspond to an adjacent samples.
(a) To design a 3-tap transversal equalizer that forces the ISI to be zero at one sampling point on each side of the mainlobec which will be given below as -
[ 0 ] = [ 1 -0.2 0.3 ] [ C-1 ]
[ 1 ] = [ 0.4 1 -0.2 ] [ C0 ]
[ 0 ] = [ -0.1 0.4 1 ] [ C1 ]
(b) Assuming that the filter taps are C-1 = 0.2593, C0 = 0.8347 and C1 = 0.3079.
Each sample can be calculated from the following equation -
Z (-4) = [ 0.1 0 0 ]
Z (-3) = [ 0.3 0.1 0 ]
Z (-2) = [ -0.2 0.3 0.1 ]
Z (-1) = [ 1 -0.2 0.3 ] [ 0.2593 ]
Z (0) = [ 0.4 1 -0.2 ] [ 0.8347 ]
Z (1) = [ -0.1 0.4 1 ] [-0.3079 ]
Z (2) = [ 0.1 -0.1 0.4 ]
Z (3) = [ 0 0.1 0 ]
Z (4) = [ 0 0 0.1 ]
Therefore, Z (-1) = 0 , Z (0) = 0 and Z (1) = 0
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