A transversal equalizer with K taps has an impulse response where T is the delay between adjacent...

A transversal equalizer with K taps has an impulse response

where T is the delay between adjacent taps, and a transfer function

The discrete Fourier transform (DFT) of the equalizer coefficients {ck} is defined as

a. Show that bk = ck, by substituting for En in the above expression.

b. From the relations given above, derive an equivalent filter structure having the z transform

c. If E(z) is considered as two separate filters E1(z) and E2(z) in cascade, sketch a block diagram for each of the filters, using z−1 to denote a unit of delay.

d. In the transversal equalizer, the adjustable parameters are the equalizer coefficients{ck}. What are the adjustable parameters of the equivalent equalizer in (b), and how are they related to {ck}?