How to generate odd frequency sinusoid input using idinput

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soeren graabaek 2023-7-3

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评论： soeren graabaek 2023-7-11

Hi,

I am trying to generate a multisinusoid input signal with odd frequencies for non-linear system identification, as recommended in [1]. Going though the documentation of the System Identification Toolbox, i found the idinput function which allow you to generate a multisinusoid signal. According to the doccumentation [2], the function is designed to also generate even/odd frquences using the parameter "GridSkip", but I cannot figure out how to use the parameter. Can someone help me with some understanding of how this parameter works?

[1]: "Nonlinear system identification: a user-oriented road map" Johan Schoukens and Lennart Ljung, IEEE control system magazine 2019

[2]:

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Answer 1

Mathieu NOE 2023-7-10

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I don't have anything against idinput , but why can't you do this directly with some basic code :

f = (1:2:7); % odd frequencies (array)

ampl = ones(size(f))./f; % amplitude (here decreasing in 1/f law)

dt = 1e-3;

samples = 5e3;

t = (0:samples-1)'*dt;

y = [];

for ci = 1:numel(f)

y = [y ampl(ci)*sin(2*pi*f(ci)*t)];

end

% signal sum of all frequencies and normalisation to +/- 1 amplitude

y = sum(y,2);

y = y./max(abs(y));

plot(t,y)

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Mathieu NOE 2023-7-10

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fyi , some methods that can help you reduce the crest factor of the signal

clc
clearvars
f = (1:2:7); % odd frequencies (array)
ampl = ones(size(f))./f; % amplitude (here decreasing in 1/f law)
dt = 1e-3;
samples = 5e3;
t = (0:samples-1)'*dt;
% %multitone signals with low crest factor and as suggested in the Boyd's paper : quadratic phase distribution:
% % phas=pi*(f-1).^2/(numel(f)); % the original version 
% phas=pi*(f-1).^2/(numel(f))^2; % I prefer this one 
% % or Shapiro Rudin method 
phas = shapiro(numel(f));
y = [];
for ci = 1:numel(f)
    y = [y ampl(ci)*sin(2*pi*f(ci)*t+phas(ci))];
end
% signal sum of all frequencies and normalisation to +/- 1 amplitude
y = sum(y,2);
y = y./max(abs(y));
plot(t,y)
y_rms = sqrt(mean(y.^2));
CF = max(abs(y))/y_rms % compute crest factor of y 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function myphase = shapiro(n) %#ok<*DEFNU>
% phase according to Shapiro Rudin method (minimize crest factor)
if n == 1
   myphase = 0;
else
   
% initialisation
str = [1 1];
k = ceil(log(n)/log(2));
for ci = 1:k-1
   l =length(str);
   str2 = str;
   str2(l/2+1:l) = -str(l/2+1:l);
   str = [str str2];
end
mystr = str(1:n);
myphase= zeros(1,n);
ind = mystr==-1;
myphase(ind)  = pi;
end
end