1. Question 3
A digital, time discrete channel with intersymbol interference (ISI) has the following impulse response h = [h-1, h0, h1]T = [-0.25, 1, 0.75]T. (.)T is the matrix transpose. The ISI is being suppressed by zero-forcing equalizer with five taps w = [w-2, w-1, w0, w1, w2]T.
Find the equalizer taps, w according to the zero-forcing (ZF) criterion with the desired equalizer response z = [0, 0, 1, 0, 0]T.
If a single discrete pulse with amplitude 1 is being sent through the channel h, what is the system response before and after ZF equalization?

2. System block diagram y x
Channel h
ZF equalizer w z

3. Expanding the convolution

4. Convolution in matrix form

5. Zero forcing equalizer

6. Before ZF equalizer

7. After ZF equalizer