pkg load signal
graphics_toolkit gnuplot
 M = 1000;
 darkgreen = [33 150 33]/256;
 interpolation_factor = 4;

% Generate M+1 samples of a Gaussian window (filter type not important)
 filter = .3*exp(-.5*(((0:M)-M/2)/(.4*M/2)).^2);
% Sample the window.
 N=24;
 sam_per_hop = M/N;
 window_dots = filter(1+(0:N)*sam_per_hop);
 normalize   = sum(window_dots)/interpolation_factor;

 window_scale_factor = 0.5;
 sam_per_hop = sam_per_hop*window_scale_factor;
 
%------------------------------------------------------------------
 figure("position", [100 200 900 600])

% Plot the continuous filter function
 xoffset = sam_per_hop*15;
 yoffset = 0.1;
 
 plot(xoffset+(0:M)*window_scale_factor, yoffset+filter,  "linestyle",":", "linewidth",1, "color","black")
 set(gca, "xaxislocation", "origin")
 xlim([0 M])
 ylim([-.06 .45])                    % allows space for negative samples (in case I change the signal)
 set(gca, "ygrid","off");
 set(gca, "xgrid","on");
 set(gca, "ytick",[0], "fontsize",14);
 xticks = [0:4*sam_per_hop:M];
 set(gca, "xtick",xticks)
 set(gca,"xticklabel",[0:length(xticks)])

% Plot the filter coefficients
 hold on
 plot(xoffset+(0:N)*sam_per_hop, yoffset+window_dots,  "color","red", ".", "markersize",10)

% Create signal to be interpolated
 samples_per_cycle = 4*M;
 signal = .2*sin(2*pi*(0:M)/samples_per_cycle);

 signal_dots = signal(1:sam_per_hop:end);
% Simulate "inserted zeros", for display
 signal_dots(2:4:end) = 0;
 signal_dots(3:4:end) = 0;
 signal_dots(4:4:end) = 0;

% Plot the data
 L = length(signal_dots);
 plot((0:L-1)*sam_per_hop, signal_dots,  "color","blue", ".", "markersize",10)
 
% Compute dot product, and plot it
 dot_product = sum(window_dots(24:-4:4).*signal_dots(17:4:37))/normalize;
 x = 27*sam_per_hop;
 plot(x, dot_product, "color",darkgreen, ".", "markersize",14)
 plot([x,x],[0,.45]);                                   % vertical line
 
% xlabel('\leftarrow  n  \rightarrow', "fontsize",16)
 text(465, -.05, '\leftarrow  n  \rightarrow', "fontsize",16)
 text(18, .1, "X[n]", "fontsize",16, "color","blue")

 title("Multirate interpolation filter", "fontsize",16, "fontweight","normal");