continuous wavelet transform without using inbuilt function cwt()

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Monika Gupta 2017-3-12

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https://ww2.mathworks.cn/matlabcentral/answers/329421-continuous-wavelet-transform-without-using-inbuilt-function-cwt

评论： Ameen Bin Obadi 2020-5-26

I need to implement continuous wavelet transform without using the inbuilt function cwt(). here g is complex morlet wavelet. b,a is shift and scale parameter respectively. s(b,a)= 1/a ∫s(t) *g ((t-b)/a) dt

I'm not allowed to use fft. I tried implementing this using convolution, but not getting right results. please help.

if true
  %%user CWT
clear all
N=300;                %sample point numbers
t=linspace(0,30,N);
%%signal
x=5*sin(2*pi*0.5*t);  % signal with freq of 0.5 HZ
%%cwt
  fc=1;fb=15;
% psi=((pi*fb)^(-0.5)).*exp(2*1i*pi*fc.*...
%     t).*exp(-t.^2/fb);
%%convolution Psi([N-n]/S)*x(n) so we calculate convolution(psi(n/s),x(n))
  for s=1:60   %scale vector s=[1:1:60]
for i = 1:N      % number of discrete times
     for k = 1:i 
             if ((i-k+1)<N+1) && (k <N+1)
              PSI = ((pi*fb)^(-0.5)).*exp(2*1i*pi*fc.*...
     (t/s)).*exp(-(t/s).^2/fb);   
                      c(i,s) = c(i)+ x(k)*PSI(i-k+1);
              end
     end
end
  end
end

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Ameen Bin Obadi 2020-5-26

I have done it but using different method. I used conv function and it worked. the conv function does the shifting for you so you only need to care about scaling.

Ameen Bin Obadi 2020-5-26