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Advanced Digital Signal Processing and Digital Communications

a.    Determine the impulse response h (t)
Sketch x(t) and h(t) on functions of time
The filter is matched with (mf) linear
The filter is designed to provide Max signal to move power ratio at its output for a given the transmitted wave form.

X(t)
t/2    T    ½ t    t

Impulse response h(t) = x(t-T)
Signal wave form
Mirror the signal wave form
x(-t)
A/2

-t    t
-T/2    -A
B) Suppose the signal x(t) is applied to the match filter h(t). Graphically  determine and filter the filter output v(t) as function of time.
The y(t) =h(t) × x(t)

A/2    X(T-t)= h(t)

-A    t/2    T

c.    PSD= No/2
Energy beyond Eb of s(t) and s(-t)
Since the signals are antipodal S1(t) = – s2(t)1the epitome threshold value is 0 i.e y0=0.
The correlater receiver is

Average energy

Input signed is changed to
X(t) =      A              0<t=T/2
-A/2       T/2<t=T/2
Impact of the change on the BER of the binary communication system
Since signal becomes unipolar,
Eb no increase by 3db

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