Convolution - Sweep Scale   Convolution would be the one of the most important operations in engineering math. If you don't have any prior study and understanding on how Convolution works, it would not be easy to make sense out of it. For those who is not familiar with Convolution, I would suggest you to go through my descriptive note here.

 Followings are the code that I wrote in Octave to creates all the plots shown in this page. You may copy these code and play with these codes. Change variables and try yourself until you get your own intuitive understanding.   < Code 1 >   x = [0 0.4 0.0 0.4 0.0];   sf = 20; % samples per bit   p_x = x;   if sf > 1    for i = 2:sf      p_x= [p_x ; x];    end    p_x = reshape(p_x,[],1);   end   a = 0.9; t = 0:10; k = 0.3; chan = 1.0 * [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];   cs = 100   hFig = figure(1,'Position',[300 300 700 600]);   subplot(4,2,1); stem(p_x,'MarkerFaceColor',[0 0 1],'color','blue'); axis([1 length(p_x) -1.0 1.0]); title("data"); box on; set(gca,'xticklabel',[]); set(gca,'yticklabel',[]); set(gca,'xtick',[]); set(gca,'ytick',[]);   subplot(4,2,2); stem(chan,'MarkerFaceColor',[1 0 0],'MarkerEdgeColor',[1 0 0],'color','red'); axis([1 length(p_x) -2.0 2.0]); title("kernel"); box on; set(gca,'xticklabel',[]); set(gca,'yticklabel',[]); set(gca,'xtick',[]); set(gca,'ytick',[]);   subplot(4,2,[3 8]); hold on; s = p_x; for i = 0:100     if i < length(p_x)        line([i i],[5 5+s(i+1)],'color','blue');        plot(i,5+s(i+1),'bo');     end;    end; line([-40 140],[5 5],'color','green');   k = flip(chan); ks = length(k);   for i = 0:100     if i < length(k)        line([i-ks+cs i-ks+cs],[3 3+k(i+1)],'color','red');        plot(i-ks+cs,3+k(i+1),'ro');     end;    end;   line([-40 140],[3 3],'color','green');   y = conv(p_x(1:min([length(p_x) cs])),chan(1:min([length(chan) cs]))); y = y(1:cs); for i = 0:200     if i < length(y)        line([i i],[1 1+y(i+1)],'color','black');        plot(i,1+y(i+1),'ko');     end;    end; line([-40 140],[1 1],'color','green');   rdx = min(cs,length(k)); rdy = 3.0; rx = cs-rdx; ry = 2.9; rectangle('Position',[rx ry rdx rdy]);   line([cs cs],[1 1+y(end)],'color','red','LineWidth',3, 'Marker','o'); line([cs cs],[1 1+2],'color','red','LineWidth',0.5);   hold off; axis([-50 150 0 6]); tStr = sprintf("step = %d",cs); title(tStr); box on; set(gca,'xticklabel',[]); set(gca,'yticklabel',[]); set(gca,'xtick',[]); set(gca,'ytick',[]);