%  Convolution Tool  (L Braile, October 2001; revised January 2002)
% define signals each 201 points long, dt=0.01
dt=0.01;
t=0:dt:2;
%
% b1 short boxcar
b1=[zeros(1,75) ones(1,51) zeros(1,75)];
% b2 long boxcar
b2=[zeros(1,50) ones(1,101) zeros(1,50)];
% sq square wave
sq=[zeros(1,75) ones(1,25) -1*ones(1,25) zeros(1,76)];
% sp spike
sp=[zeros(1,100) 1 zeros(1,100)];
% st step function
st=[zeros(1,50) ones(1,151)];
% ra random number
ra=randn(1,201);
ramax=max(abs(ra));
ra=ra/ramax;
% un uniformly distributed random number
un=rand(1,201);
un=2*un - 1;
% c1 low frequency cosine
c1=cos(2*pi*1*t);
% c2 high frequency cosine
c2=cos(2*pi*5*t);
% si sin x/x or sinc function
sit=sin(2*pi*4*t(2:101))./(2*pi*4*t(2:101));
si=[fliplr(sit) 1 sit];
% df differentiation operator
df=[zeros(1,99) 1 -1 zeros(1,100)];
% t1 short triangle
tr1=[1:1:26]/26;
tr2=[25:-1:1]/26;
t1=[zeros(1,75) tr1 tr2 zeros(1,75)];
% t2 long triangle
tr1=[1:1:51]/51;
tr2=[50:-1:1]/51;
t2=[zeros(1,50) tr1 tr2 zeros(1,50)];
% ga, gaussian
ga1=exp(-(8*t(2:101).*t(2:101)));
ga=[fliplr(ga1) 1 ga1];
% cb cosine bell
nsw=100;
   for i = 1:nsw
      j = nsw-i;
      fa1(i) = 0.5*(cos(pi*j/nsw) + 1);
   end
cb=[fa1 1 fliplr(fa1)];
% ex exponential
thalf=0.25;
x1=t(2:151)*0.696/thalf;
ex1=exp(-x1);
ex=[zeros(1,50) 1 ex1];
% w1 Ricker wavelet
[rk]=ricker(201,20,dt,0,25);
rmax=max(abs(rk));
w1=rk/rmax;
% w2 Ricker wavelet
[rk]=ricker(201,80,dt,0,25);
rmax=max(abs(rk));
w2=rk/rmax;
% s1 spike series 1
s1=[zeros(1,10) 1 zeros(1,80) -0.7 zeros(1,100) 0.4 zeros(1,8)];
% s2 spike series 2
s2=[zeros(1,10) 1 zeros(1,45) .4 zeros(1,34) -0.7 zeros(1,55) ...
      -.3 zeros(1,44) 0.4 zeros(1,8)];
% s3 spike series 3
s3=[zeros(1,50) 1 zeros(1,8) -0.2 zeros(1,9) 0.7 zeros(1,8) -0.8 zeros(1,5) 0.3...
      zeros(1,12) -0.4 zeros(1,8) 0.25 zeros(1,5) 0.1 zeros(1,9) -0.1 zeros(1,6)...
      0.1 zeros(1,71)];
% rp ramp
rp1=[1:1:101]/101;
rp=[zeros(1,50) rp1 zeros(1,50)];
% sw sweep 1-5 Hz, 1000 points, dt=0.01
for i=1:183
   ti=(i-1)*dt;
   f=2 + 1*(ti);
   sw1(i)=sin(2*pi*f*ti);
end
sw=[zeros(1,9) sw1 zeros(1,9)];
% di Dirac comb
di=[zeros(1,10) 1 zeros(1,19) 1 zeros(1,19) 1 zeros(1,19) 1 zeros(1,19) 1 ...
   zeros(1,19) 1 zeros(1,19) 1 zeros(1,19) 1 zeros(1,19) 1 zeros(1,19) 1 ...
   zeros(1,10)];
% w3 wavelet - signal n=2
ts=0.21; n=2; npts=201; na=25; thalf=0;
[w3]=signal(ts,dt,n,0,npts,na,thalf);
% w4 wavelet - signal n=4
ts=0.41; n=4; npts=201; na=25; thalf=0;
[w4]=signal(ts,dt,n,0,npts,na,thalf);
% w5 wavelet - signal n=5
ts=0.51; n=5; npts=201; na=25; thalf=0;
[w5]=signal(ts,dt,n,0,npts,na,thalf);
% w6 wavelet - signal n=7
ts=0.71; n=7; npts=201; na=25; thalf=0;
[w6]=signal(ts,dt,n,0,npts,na,thalf);
% w7 wavelet - signal n=7 thalf=0.15
ts=0.71; n=7; npts=201; na=25; thalf=0.15;
[w7]=signal(ts,dt,n,0,npts,na,thalf);
% w8 wavelet - signal n=9 thalf=0.2
ts=0.91; n=9; npts=201; na=25; thalf=0.2;
[w8]=signal(ts,dt,n,0,npts,na,thalf);
%
%
% plot signals
figure
subplot(5,6,1), plot(t,b1,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'b1, boxcar','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
%
subplot(5,6,2), plot(t,b2,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'b2, boxcar','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,3), plot(t,sq,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
title('                        Functions and Signals for Convolution and Correlation Tool',...
   'fontweight','bold','fontsize',12)
text(0.1,-0.9,'sq, sq. wave','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,4), plot(t,sp,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'sp, spike','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,5), plot(t,df,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'df, differentiator','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,6), plot(t,st,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'st, step func.','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,7), plot(t,ra,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'ra, random nor.','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
%
subplot(5,6,8), plot(t,un,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'un, random unif.','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,9), plot(t,c1,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'c1, cosine','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,10), plot(t,c2,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'c2, cosine','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,11), plot(t,si,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'si, sinc func.','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,12), plot(t,t1,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'t1, triangle','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,13), plot(t,t2,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'t2, triangle','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
ylabel('Relative Amplitude','FontWeight','bold')
%
subplot(5,6,14), plot(t,ga,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'ga, gaussian','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,15), plot(t,cb,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'cb, cosine bell','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,16), plot(t,ex,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'ex, exponential','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,17), plot(t,rp,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'rp, ramp','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,18), plot(t,di,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'di, dirac comb','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,19), plot(t,s1,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'s1, spike series','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
%
subplot(5,6,20), plot(t,s2,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'s2, spike series','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,21), plot(t,s3,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'s3, spike series','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,22), plot(t,sw,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'sw, sweep','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,23), plot(t,w1,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w1, ricker wavelet','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,24), plot(t,w2,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w2, ricker wavelet','FontWeight','bold')
set(gca,'XTickLabelMode','manual','XTickLabel',[])
set(gca,'YTickLabelMode','manual','YTickLabel',[])
%
subplot(5,6,25), plot(t,w3,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w3, wavelet','FontWeight','bold')
xlabel('Time (s)','FontWeight','bold')
%
subplot(5,6,26), plot(t,w4,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w4, wavelet','FontWeight','bold')
set(gca,'YTickLabelMode','manual','YTickLabel',[])
xlabel('Time (s)','FontWeight','bold')
%
subplot(5,6,27), plot(t,w5,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w5, wavelet','FontWeight','bold')
set(gca,'YTickLabelMode','manual','YTickLabel',[])
xlabel('Time (s)','FontWeight','bold')
%
subplot(5,6,28), plot(t,w6,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w6, wavelet','FontWeight','bold')
set(gca,'YTickLabelMode','manual','YTickLabel',[])
xlabel('Time (s)','FontWeight','bold')
%
subplot(5,6,29), plot(t,w7,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w7, wavelet','FontWeight','bold')
set(gca,'YTickLabelMode','manual','YTickLabel',[])
xlabel('Time (s)','FontWeight','bold')
%
subplot(5,6,30), plot(t,w8,'r-','linewidth', 1.5), axis([0 2 -1.1 1.1])
text(0.1,-0.9,'w8, wavelet','FontWeight','bold')
set(gca,'YTickLabelMode','manual','YTickLabel',[])
xlabel('Time (s)','FontWeight','bold')
%
%
pause
%
%
while 1
%
n1=input('Type 1 for convolution or 2 for correlation  or q to quit ','s');
%
  if strcmp(n1,'q') | strcmp(n1,'Q'), break, end
%
nc=str2num(n1);
sig1=input('Type 2 character name for first signal ');
sig2=input('Type 2 character name for second signal ');
to=0:dt:4;
% Convolution
if nc==1
   out=conv(sig1,sig2);
   outmax=max(abs(out));
   out=out/outmax;
end
% Correlation
if nc==2
   out=xcorr(sig1,sig2);
   outmax=max(abs(out));
   out=out/outmax;
end
% Plot selected signals and output
figure
subplot(2,2,1), plot(t,sig1,'r-','linewidth', 1.5), axis([0 4 -1.1 1.1])
title('Signal 1','FontWeight','bold')
xlabel('Time (s)','FontWeight','bold')
ylabel('Relative Amplitude','FontWeight','bold')
subplot(2,2,2), plot(t,sig2,'r-','linewidth', 1.5), axis([0 4 -1.1 1.1])
title('Signal 2','FontWeight','bold')
xlabel('Time (s)','FontWeight','bold')
ylabel('Relative Amplitude','FontWeight','bold')
if nc==1
   subplot(2,2,3), plot(to,out,'r-','linewidth', 1.5), axis([0 4 -1.1 1.1])
   title('Convolution of Signals 1 and 2','FontWeight','bold')
   xlabel('Time (s)','FontWeight','bold')
   ylabel('Relative Amplitude','FontWeight','bold')
end
if nc==2
   subplot(2,2,3), plot(to,out,'r-','linewidth', 1.5), axis([0 4 -1.1 1.1])
   title('Correlation of Signals 1 and 2','FontWeight','bold')
   xlabel('Time (s)','FontWeight','bold')
   ylabel('Relative Amplitude','FontWeight','bold')
end
%
end