FIR is a class of LTI filter and the transfer function of the filter is

Now consider an FIR filter having length M can be expressed as

= =

We obtained the impulse response with

The impulse response of finite length M . FIR

filter have only Zeros .FIR filter is also known as all zeros filter or feed

forward or non -recursive or transversal.

For linear phase response FIR digital

filter satisfies the following condition

we have to

know that

Inverse

Discrete time Fourier transform

For high

pass filter limit breakdown into two interval

since sin(n)=0

so above equation become

Where

and

Impulse

response shows non-causal behaviour and to

convert it into causal system by giving

a delay . Delaying term convert into

linear phase and causal .

for odd

The impulse

response truncation is equal to multiplying the

by the

selecting window. In given case the stop

band attenuation is 74db which is near to the Blackman window.

Blackman

window mathematical expression can be expressed as

for

The final

expression for is

Designing parameters of high pass filter:

Stopband : 0-2.5 kHz

Passband : 3

kHz

Sampling

rate: 10 kHz

Stopband

attenuation:72 dB

Sol:

According

to the stopband attenuation -72dB we select the Blackman window.

for

For M=110

for

The final

output can be expressed as

n

0

-0.00819

-0.08

0.000652

1

.

.

.

2

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

109

.

.

.

Matlab

Code:

>> L=110;

>> Xc=0.55;

>> Qn=blackman(L+1);

>> p=fir1(L,Xc,’high’ ,Qn);

>> freqz(p)

Outp