N

h(t) = L wk8( t - kT)

k=-N

The impulse response of the cascaded system is given by the convolution sum

N

e; = L WjCn_ j

j=-N

where Pn = p(n1). The kth sample of the output of the cascaded system due to the input

sequence {In} is defined by

t, = POlk + L i.r,.;nie-k

where Poh is a scaled version of the desired symbol h. The summation term L I»Pk _ n isn""k

the intersymbol interference.

The peak value of the interference is given by

N N N

D(N) = L Ipnl = L L wkcn_ k

n=-N n=-N k=-Nn""O n ie-O

To make the lSI equal to zero, we require

N

P n = L wkcn_k

k=-N

= { 1,0,

n = °nt:O }

(b) By taking the z-transform of the convolution sum

N

L wkcn_ kk=- N

and recalling that convolution in the discrete-time domain is transformed into multiplicationin the z-domain, we get

P(z) = H(z)C(z)

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