dc

3. Simplify receiver design
Because the transmitter has an integrator , the receiver
consists simply of a low-pass filter.
(The differentiator in the conventional DM receiver is cancelled by the integrator )
Linear Prediction (to reduce the sampling rate):
Consider a finite-duration impulse response (FIR)
discrete-time filter which consists of three blocks :
1. Set of p ( p: prediction order) unit-delay elements (z-1)
2. Set of multipliers with coefficients w1,w2,…wp
3. Set of adders ( )
The filter output (The linear
Find
xˆ
n
The prediction error is
e
n xn
xˆ
n
Let the index of
w , w
1
2
k 1
2
, ,
w
performance be
n
x(
n k)
(mean square error) (3.61)
to minimize J
From(3.59) (3.60) and (3.61) we have
p
2
x
n
2 w Exnxn
k
J E
Assume X ( t) is stationary
p
J E e
w
k
p
k 1
k
predition of the input ) is
(3.59)
(3.60)
processwith zero mean ( E[
x[
n]]
0)