PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

590 Practical MATLAB® Applications for Engineers

R.6.120 Type-1 FIR fi lter is defi ned by the following relation:

h(n) = h(N − n) for 0 ≤ n ≤ N − 1, with N = odd.

Then the amplitude response is given by

H(W) 11 
 a(n)cos(W)n



e jNW

n

N

2

0

2

∑

where a 1 ( 0 ) = h(N/ 2 ) is the mid-point and a 1 (n) = 2 h((N/ 2 ) − n) for 1 ≤ n ≤ N/ 2.

Type-1 FIR fi lters can be used to design any fi lter type. The following sequence

illustrates a type-1 FIR fi lter:

h(n)
 0.09

(n) 0.30(n )^1 0.3593
(n^2 )0.30
(n 3)0.09
(nn)^4

R.6.121 The type-2 FIR fi lter is defi ned by

h(n) = h(N − n) for 0 ≤ n ≤ N − 1, with N = even

then

H(W) 22 
 a(n)cosW(n 12 )



e jNW

n

N

2

0

12

[]

()

∑

where

an h

N

2 ()
 nn (N)



2 

1

2

  12 1 2







for = , ,...

Since the response is defi ned for −π ≤ W ≤ π, then

H(W^2

)^0

Therefore, type-2 FIR fi lters cannot be used to implement an HP or a BP fi lter.

The following sequence illustrates a type-2 FIR fi lter:

h(n) = −0.09δ(n) + 0.30δ(n − 1 ) + 0.3593δ(n − 2 ) + 0.3593δ(n − 3 )

• 0.30δ(n − 4 ) −0.09δ(n − 5 )

R.6.122 The type-3 FIR fi lter is defi ned by

h(n) = −h(N − n) for 0 ≤ n ≤ N, with N = odd

H (W) 33 
 [a (n)sin(Wn)]



eejNW j

n

N

22

1

2

 ∑

where a 3 (n) = 2 h (^) [ N__
2
− n] for n = 1, 2, ... N/2)