Normalize graph chebyshev filter

Hello, I have this code that corresponds to an analog chebyshev low pass filter, which must have a cutoff frequency of 250 Hz at 0.7, when graphing with freqs I get a signal that does not cut at 0.7. ¿How do I normalize the filter to match the point (250,0.7)?

n = 3; Rp = 0.5;

Wn = [250 2000];

[b a]=cheby1(n,Rp,Wn,'s')

[h,w]=freqs(b,a)

plot(w,abs(h))

[Juan Chehin]

try this code but it doesn't work either

Fs = 4400;

Fn = Fs/2;

n = 3; Rp = 0.5;

Wn = [250 2000]/Fn;

[b a]=cheby1(n,Rp,Wn,'s')

[h,w]=freqs(b,a)

plot(w,abs(h))

[Star Strider]

Chebyshev filter passbands and stopbands are defined differently than for other filters. The stopband is the frequency at which the filter characteristic equals the passband ripple amplitude, not the -6 dB point as with other filter types.

Answer 1

[Mathieu NOE]

hello

I tried an iterative correction method . I plot the frf of the filter in dB and 0.7 then correspond to the - 3 dB cutoff amplitude.

Got a good result within 8 iterations :

Code :

n = 3; Rp = 0.5;
Wn = [250 2000];
[b a]=cheby1(n,Rp,Wn,'s') ;
w = logspace(2,4,300); % Frequency vector
[h,ww]=freqs(b,a,w) ;
FRF_dB = 20*log10(abs(h));
FRF_dB2 = FRF_dB;
semilogx(w,FRF_dB);

for ci = 1:8 % loops

    % find the - 3dB crossing points
    [f1,s0_pos,f2,s0_neg] = crossing_V7(FRF_dB2,w,-3);
    cor_coeff1 = Wn(1)/f1;
    cor_coeff2 = Wn(2)/f2;

    % 2nd iteration
    W = [W(1)*cor_coeff1 W(2)*cor_coeff2];
    [b a]=cheby1(n,Rp,W,'s') ;
    [h,ww]=freqs(b,a,w) ;
    FRF_dB2 = 20*log10(abs(h));

end
% check again the - 3dB crossing points
[f11,s0_pos,f22,s0_neg] = crossing_V7(FRF_dB2,w,-3);

semilogx(w,FRF_dB,'b',w,FRF_dB2,'r',f11,s0_pos,'dr',f22,s0_neg,'dr');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)

% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format

% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%
%	[ind,t0,s0] = ... also returns the data vector corresponding to 
%	the t0 values.
%

% check the number of input arguments
error(nargchk(1,4,nargin));

% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end

% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end

% check interpolation method input
if nargin < 4
    imeth = 'linear';
end


% make row vectors
t = t(:)';
S = S(:)';

% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;

% first look for exact zeros
ind0 = find( S == 0 ); 

% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );

% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);

% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);

if ~isempty(ind)

    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) > eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) > eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)

                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end

    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);

    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);

else

    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];

    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Addition:
% % Some people like to get the data points closest to the zero crossing,
% % so we return these as well
% [CC,II] = min(abs([S(ind-1) ; S(ind) ; S(ind+1)]),[],1); 
% ind2 = ind + (II-2); %update indices 
% 
% t0close = t(ind2);
% s0close = S(ind2);
end

[Mathieu NOE]

hello Juan

so did you check my submission ?

all the best

[Juan Chehin]

Hello Mathieu, if I was checking your answer and thank you for the same, the question is that it was not what I was looking for. What I need is to put together a chebyshev low pass filter with cutoff frequency at 250Hz, which drops to 0.707 at that point.

[Mathieu NOE]

hello Juan

well , I was maybe fooled by the fact that the code and figure in your initial post deals with a passband filter (and not a lowpass filter)

I can correct that if the real question is for only lowpass filter

[Mathieu NOE]

so this is the lowpass version

I also came back to a vertical linear scale - not dB - as it seems this was also a bit confusing.

plot :

code :

clc
clearvars

n = 3; Rp = 0.5;
Wn = [250];
threshold = 0.707;
W = Wn;
[b a]=cheby1(n,Rp,Wn,'s') ;
w = linspace(0,400,100); % Frequency vector
[h,ww]=freqs(b,a,w) ;
FRF = abs(h);
FRF2 = FRF;
semilogx(w,FRF);
for ci = 1:8 % loops
    % find the "threshold" crossing point~
    [f1,s0_pos,f2,s0_neg] = crossing_V7(FRF2,w,threshold);
    cor_coeff1 = Wn(1)/f2;
    % 2nd iteration
    W = W(1)*cor_coeff1;
    [b a]=cheby1(n,Rp,W,'s') ;
    [h,ww]=freqs(b,a,w) ;
    FRF2 = abs(h);
end
% check again the "threshold" crossing point
[f11,s0_pos,f22,s0_neg] = crossing_V7(FRF2,w,threshold);
plot(w,FRF,'b',w,FRF2,'r',f11,s0_pos,'dr',f22,s0_neg,'dr');
legend('initial design','final design');
xlabel('Frequency (Hz)');
ylabel('Modulus');
title('Filter FRF ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)
% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format
% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%
%	[ind,t0,s0] = ... also returns the data vector corresponding to 
%	the t0 values.
%
% check the number of input arguments
error(nargchk(1,4,nargin));
% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end
% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end
% check interpolation method input
if nargin < 4
    imeth = 'linear';
end
% make row vectors
t = t(:)';
S = S(:)';
% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;
% first look for exact zeros
ind0 = find( S == 0 ); 
% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );
% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);
% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);
if ~isempty(ind)
    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) > eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) > eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)
                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end
    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);
    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);
else
    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];
    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Addition:
% % Some people like to get the data points closest to the zero crossing,
% % so we return these as well
% [CC,II] = min(abs([S(ind-1) ; S(ind) ; S(ind+1)]),[],1); 
% ind2 = ind + (II-2); %update indices 
% 
% t0close = t(ind2);
% s0close = S(ind2);
end

[Mathieu NOE]

hello Juan

if my answer has fullfilled your expectations, do you mind accepting it ?

thanks

[Juan Chehin]

ready, I accepted it

[Mathieu NOE]

thanks !!