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FIR Systems are represented in four different ways
1. Direct Form Structures
2. Cascade Form Structure
3. Frequency-Sampling Structures
4. Lattice structures.

**STRUCTURES FOR FIR SYSTEMS**

FIR
Systems are represented in four different ways

1. Direct
Form Structures

2. Cascade
Form Structure

3. Frequency-Sampling
Structures

4. Lattice
structures.

**DIRECT FORM STRUCTURE OF FIR SYSTEM**

The above
equation can be expanded as,

Y(n)=
h(0) x(n) + h(1) x(n-1) + h(2) x(n-2) + …………… + h(M-1) x(n-M+1) (2)

Implementation
of direct form structure of FIR filter is based upon the above equation.

1. There
are M-1 unit delay blocks. One unit delay block requires one memory location.

Hence
direct form structure requires M-1 memory locations.

2. The
multiplication of h(k) and x(n-k) is performed for 0 to M-1 terms. Hence M
multiplications and M-1 additions are required.

3. Direct
form structure is often called as transversal or tapped delay line filter.

**CASCADE FORM STRUCTURE OF FIR SYSTEM**

In
cascade form, stages are cascaded (connected) in series. The output of one
system is input to another. Thus total K number of stages are cascaded. The
total system function 'H' is given by

H= H1(z)
. H2(z)……………………. Hk(z) (1)

H=
Y1(z)/X1(z). Y2(z)/X2(z). ……………Yk(z)/Xk(z) (2)

Each H1(z),
H2(z)… etc is a second order section and it is realized by the direct form as
shown in below figure.

System
function for FIR systems

Expanding
the above terms we have

H(z)=
H1(z) . H2(z)……………………. Hk(z)

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