Design a high pass filter using kaiser window

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

Answer 1

[John BG]

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

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thanks in advance

John BG

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