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Discrete Wavelet Transforms

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Digital Signal Processing

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Abstract

Fourier transform has been extensively used in signal processing to analyze stationary signals. A serious drawback of the Fourier transform is that it cannot reflect the time evolution of the frequency.

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Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Vasavi College of Engineering (affiliated to Osmania University), Hyderabad, Telangana, India

    K. Deergha Rao

  2. Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada

    M.N.S. Swamy

Authors
  1. K. Deergha Rao
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  2. M.N.S. Swamy
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Corresponding author

Correspondence to K. Deergha Rao .

Appendix

Appendix

  • blocksize.m

  • _______________________________________________________________

  • %Here watermark image is referred with 8x8 block size

  • function [rw1 cw1 rc cc]=blocksize(wg,H2)

  • w1=mod(size(wg,1),8);

  • w2=mod(size(wg,2),8);

  • if(w1==0)

  •     w1=w1+8;

  • end;

  • if(w2==0)

  •     w2=w2+8;

  • end;

  • rw=(size(wg,1)-w1)/8;

  • rw1=rw;

  • cw=(size(wg,2)-w2)/8;

  • cw1=cw;

  • c1=mod(size(H2,1),rw);

  • c2=mod(size(H2,2),cw);

  • if(c1==0)

  •     c1=mod(size(H2,1),rw+1);

  •     rw1=rw+1;

  • end;

  • if(c2==0)

  •     c2=mod(size(H2,2),cw+1);

  •     cw1=cw+1;

  • end;

  • rc=(size(H2,1)-c1)/rw1;

  • cc=(size(H2,2)-c2)/cw1;

  • embed.m

  • -----------------------------------------------------------------------------------------------

  • function H2=embed(key,wg,H2,rw1,cw1,rc,cc)

  • g=2;

  • rand(′state′,key);

  • cr1=1;

  • wr1=1;

  • wmd1=[];

  • for i=1:rw1

  •     wmd2=[];

  •     cr2=i*rc;

  •     wr2=i*8;

  •     if(i==rw1)

  •         cr2=size(H2,1);

  •         wr2=size(wg,1);

  •     end;

  •     cc3=1;

  •     wc3=1;

  •     for j=1:cw1

  •         cc4=j*cc;

  •         wc4=j*8;

  •         if(j==cw1)

  •             cc4=size(H2,2);

  •             wc4=size(wg,2);

  •         end;

  •         h=H2(cr1:cr2,cc3:cc4);

  •         msg=wg(wr1:wr2,wc3:wc4);

  •         msg=reshape(msg,size(msg,1)*size(msg,2),1);

  •      for k=1:length(msg)

  •             pn=3*round(2*(rand(size(h,1),size(h,2))-0.5)); % generation of PN sequence

  •             if msg(k)==0

  •                 h=h+g*pn;

  •             end;

  •         end;

  •         wmd2=[wmd2 h];

  •         cc3=cc4+1;

  •         wc3=wc4+1;

  •     end;    

  •     wmd1=[wmd1;wmd2];

  •     cr1=cr2+1;

  •     wr1=wr2+1;

  • end;

  • H2=wmd1;

  • extract.m

  • -----------------------------------------------------------------------------------------------

  • function extract=extract(key,wg,H3,rw1,cw1,rc,cc)

  • g=2;rand(′state′,key);cr1=1;wr1=1;p=1;correlation=ones(size(wg,1)*size(wg,2),1);

  • for i=1:rw1

  •     cr2=i*rc;  wr2=i*8;

  •     if(i==rw1)

  •         cr2=size(H3,1); wr2=size(wg,1);

  •     end;

  •     cc3=1; wc3=1;

  •     for j=1:cw1

  •         cc4=j*cc;wc4=j*8;

  •         if(j==cw1)

  •             cc4=size(H3,2);wc4=size(wg,2);

  •         end;

  •      h=H3(cr1:cr2,cc3:cc4);msg=wg(wr1:wr2,wc3:wc4);msg=reshape(msg,size(msg,1)*size(msg,2),1);

  •         for k=1:length(msg)

  •             pn=3*round(2*(rand(size(h,1),size(h,2))-0.5)); % generation of PN sequence

  •             correlation(p)=corr2(h,g*pn);p=p+1;

  •         end;

  •         cc3=cc4+1;wc3=wc4+1;

  •     end;    

  •     cr1=cr2+1;wr1=wr2+1;

  • end;

  • threshold=mean(abs(correlation));

  • p=1;wr1=1;

  • wmd1=[];

  • for i=1:rw1

  •     wmd2=[];wr2=i*8;

  •     if(i==rw1)

  •         wr2=size(wg,1);

  •     end;

  •     wc3=1;

  •     for j=1:cw1

  •         wc4=j*8;

  •         if(j==cw1)

  •             wc4=size(wg,2);

  •         end;

  •         msg=wg(wr1:wr2,wc3:wc4);

  •         we=ones(size(msg,1),size(msg,2));msg=reshape(msg,size(msg,1)*size(msg,2),1);

  •         for k=1:length(msg)

  •             if(correlation(p)>threshold)

  •                we(k)=0;

  •             end;

  •             p=p+1;

  •         end;

  •         wmd2=[wmd2 we];wc3=wc4+1;

  •     end;    

  •     wmd1=[wmd1;wmd2]; wr1=wr2+1;end;extract=wmd1;

  • extracthost.m

  • -----------------------------------------------------------------------------------------------

  • function H2=extracthost(key,wg,H2,rw1,cw1,rc,cc)

  • g=1;

  • rand(′state′,key);

  • cr1=1;

  • wr1=1;

  • wmd1=[];

  • for i=1:rw1

  •     wmd2=[];

  •     cr2=i*rc;

  •     wr2=i*8;

  •     if(i==rw1)

  •         cr2=size(H2,1);

  •         wr2=size(wg,1);

  •     end;

  •     cc3=1;

  •     wc3=1;

  •     for j=1:cw1

  •         cc4=j*cc;

  •         wc4=j*8;

  •         if(j==cw1)

  •             cc4=size(H2,2);

  •             wc4=size(wg,2);

  •         end;

  •         h=H2(cr1:cr2,cc3:cc4);

  •         msg=wg(wr1:wr2,wc3:wc4);

  •         msg=reshape(msg,size(msg,1)*size(msg,2),1);

  •         for k=1:length(msg)

  •             pn=3*round(2*(rand(size(h,1),size(h,2))-0.5)); % generation of PN sequence

  •             if msg(k)==0

  •                 h=h-g*pn;

  •             end;

  •         end;

  •         wmd2=[wmd2 h];

  •         cc3=cc4+1;

  •         wc3=wc4+1;

  •     end;    

  •     wmd1=[wmd1;wmd2];

  •     cr1=cr2+1;

  •     wr1=wr2+1;

  • end;

  • H 2=wmd1;

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Rao, K., Swamy, M. (2018). Discrete Wavelet Transforms. In: Digital Signal Processing. Springer, Singapore. https://doi.org/10.1007/978-981-10-8081-4_10

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