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4. Selected Applications 145

3. ADAPTIVE NOISE FILTERING USING
BACKPROPAGATION NEURAL NETWORK

Consider the signal transmitted through the noisy channel gets corrupted
with the noise. The corrupted signal is given as the input to the FIR filter as
given below to filter the noisy part of the signal.
Let x(n) be the noisy corrupted input signal to the system, y(n) be the
output signal of the system which is the filtered signal and h(n) is the impulse
response of the system. They are related mathematically as given below.

y(n) = x(n)*h(n)

⇒
N-1
y(n) = Σ h(k)x(n-k)
k=0

‘*’ is the convolution operator. ‘N’ is the order of the filter. For
instance if the order of the filter is 11,

y(n) = h(0)x(n) + h(1)x(n-1) + h(2)x(n-2) + h(3)x(n-3) + h(4)x(n-4)+
…h(10) x(n-10)

The h(0), h(1), … h(10) are the impulse response of the system, otherwise
called as the filter co-efficients of the system.
Obtaining the values of the filter co-efficients is the task involved in
designing the digital filter to do specific operation. To obtain the values
there is the need to study about the nature of the noise of the channel.
In practical situations the reference signal is sent through the channel and
the corresponding corrupted signal obtained as the output of the channel is
stored. These are used for determining the filter co-efficients of the FIR
filter. Once filter co-efficients are obtained, they are used to filter the real
time noisy signal corrupted due to channel transmission at the receiver side.

Figure 4-5. FIR FILTER