MATLAB: Design a high pass filter using kaiser window

kaiser

I could not find any documentation regarding high pass filter design using kaiser window. I need a help on this problem

Best Answer

Hi Gehan

there are different ways to build a HPF with Kaiser time windowing

1.- manually building the time window for a LPF

% 1.- LPF with desired window
wp=0.2*pi;ws=.3*pi;As=45;Ap=.3  % As and Ap in dB
tr_width=ws-wp;    % transition width
M=ceil((As-7.95)/(2.285*tr_width)+1)+1  % filter length
if As>=50       % As in dB
    beta=0.1102*(As-8.7)
end
if As<50 && As>=21
    beta=0.582*(As-21)^.4+.07886*(As-21)
end                          % mind the gag, no calculation for As<21dB
% from http://melodi.ee.washington.edu/courses/ee518/notes/lec17.pdf 
% beta controls both width and tapering off i.e. beta increasing then width
% increases but sidelobe amplitudes decrease (good)
n=[0:1:M-1]
wc=(ws+wp)/2;hd=ideal_lp(wc,M);
w_kai=(kaiser(M,beta))';h=hd.*w_kai;
[db,mag,pha,grd,w]=freqz_m(h,[1]);
delta_w=2*pi/1000;
% As=-round(max(db(ws/delta_w+[1:1:501])))   % min stop band attenuation
subplot(2,2,1);stem(n,hd);title('ideal impulse response')
axis([0 M-1 -0.1 .3]);xlabel('n');ylabel('hd(n)')
subplot(2,2,2);stem(n,w_kai);title('Kaiser time window')
axis([0 M-1 0 1.1]);xlabel('n');ylabel('w(n)')
subplot(2,2,3);stem(n,h);title('actual impulse response')
axis([0 M-1 -.1 .3]);xlabel('n');ylabel('h(n)')
subplot(2,2,4);plot(w/pi,db);title('|HkaiLPF|  dB');grid
axis([0 1 -100 10]);xlabel('frequency in pi units');ylabel('dB')

and then applying the frequency translation

That luckily I am not doing here because oh wonder MATLAB has a single command to do it all:

   HpFilt = designfilt('highpassfir','PassbandFrequency',0.3, ...
           'StopbandFrequency',0.2,'PassbandRipple',0.5, ...
           'StopbandAttenuation',45,'DesignMethod','kaiserwin');
        figure(2);fvtool(HpFilt)
  dataIn = rand(1000,1); 
      figure; subplot(2,1,1);plot(dataIn);title('input noise')
  subplot(2,1,2);plot(dataOut);title('HPF Kai filtered noise')

the LPF obtained by 'mirroring' the HPF around the transition band would be

LpFilt = designfilt('lowpassfir','PassbandFrequency',0.2, ...
         'StopbandFrequency',0.3,'PassbandRipple',0.5, ...
         'StopbandAttenuation',45,'DesignMethod','kaiserwin');
  figure(1);fvtool(LpFilt)
dataIn = rand(1000,1);
dataOut = filter(LpFilt,dataIn);
subplot(2,1,1);plot(dataIn);title('input noise')
subplot(2,1,2);plot(dataOut);title('LPF Kai filtered noise')

Gehan

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer of any help

please click on the thumbs-up vote link

thanks in advance

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

Related Solutions

MATLAB: How to Design FIR Highpass Filter in which Stopband Ripples attenuate (width) as frequency is increased

Notice that in the first plot the x-axis (frequency) scale is logarithmic and in the lower plot, linear.

Try this:

semilogx(f,db(abs(H_fir1)))

MATLAB: Design a low pass filter using kaiser window

Like Start Strider points out you can manually key in filter parameter in the fvtool GUI, but can also key in all fvtool parameters in a single MATLAB line:

LpFilt = designfilt('lowpassfir', ...
                    'PassbandFrequency',0.2, ...
                    'StopbandFrequency',30, ...
                    'PassbandRipple',0.1, ...
                    'StopbandAttenuation',44, ...
                    'SampleRate',100, ...
                    'DesignMethod','kaiserwin');
figure(1);fvtool(LpFilt)

the following filters test noise through this LPF .

    dataIn = rand(1000,1);
    dataOut = filter(LpFilt,dataIn);
    subplot(2,1,1);plot(dataIn);title('input noise')
  subplot(2,1,2);plot(dataOut);title('LPF Kai filtered noise')

would it be possible to let us the readers know what book are these exercises from?

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, please if you find this answer of any help, please click on the thumbs-up vote link,

thanks in advance for time and attention