FIR Lowpass Filter Design In Window Functions

FIR Lowpass Filter Design In Window Functions

BY JingFeng Zhao，EE

 

Typical procedure of design lowpass filter in windows:

To design a lowpass filter in windows, we should do in this procedure:

(1)   Get h_d(n), here exists three different situations:

①If we know desired frequency response H_d(ω), we just need to compute IDTFT{ H_d(ω) = h_d(n)};

②If we know desired frequency response H_d(ω), but it is very complex, or we cannot write a determinate formula for H_d(ω), we can sample M points in H_d(ω), then take M point IDTFT{ H_d(ω)}

③If we just know the stopband attenuation and the desired boundary frequency, we can use ideal filter as approximating function, then take IDTFT for this approximating function to get h_d(n).

(2) After we get h_d(n), we should determine the window function(ω(n)) according to the desire of Transition band and the stopband attenuation.

(3) h(n) = h_d(n) ω(n). Where ω(n) is finite length window function.

 

Design In MATLAB

In the preamble, I have related to the typical way of design a lowpass filter by window function. If we make a program in C language in this method, we can design the filter we needed, but it is not necessary just because we have MATLAB, with MATLAB, the design will be very easy.

Here I choose remez arithmetic. It relates to functions:

①remezord(), with this function we can get the order of filter.

②remez(), use this function we can get a sequence, actually this sequence is h(n).

Here we find the power of science computing software(such as MATLAB and SCILAB)! Yes, it make the design to be very easy and happy!

 

Here is all the source code of my design:

clear

Fs=8000;

fp=0.2*Fs/2

rp=1-10^(-0.25/20);

fs=0.3*Fs/2

rs=10^(-51/20)

f=[fp fs];

A=[1 0];

dev=[rp rs];

[n,f0,m0,w]=remezord(f,A,dev,Fs);

n

b=remez(n,f0,m0,w);

freqz(b,1,256)

%[h,w]=freqz(b,1,256,1);

%h=abs(h);

%h=20*log10(h);

%plot(w,h);

%xlabel('频率（归一化）');

%ylabel('幅度(db)');

t = (0:200)/8000;

s = sin(2*pi*t*400)+sin(2*pi*t*1500);%混和正弦波信号

sf = filter(b,1,s);

figure(2);

subplot(211)

plot(t,s);

grid on;

%xlim([0,1]);

%ylim([-4,4]);

subplot(212)

plot(t,sf);

grid on;

%xlim([0,1]);

%ylim([-4,4])