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solution manual simon haykin
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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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