Discrete Wavelet Transforms

K. Deergha Rao; M.N.S. Swamy

doi:10.1007/978-981-10-8081-4_10

Digital Signal Processing pp 619-691 | Cite as

Discrete Wavelet Transforms

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K. Deergha Rao
M.N.S. Swamy

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First Online: 14 April 2018

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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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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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Authors and Affiliations

K. Deergha Rao
- 1
Email author
M.N.S. Swamy
- 2

1.Department of Electronics and Communication EngineeringVasavi College of Engineering (affiliated to Osmania University)HyderabadIndia
2.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

Discrete Wavelet Transforms

Abstract

References

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