How to prevent envelope crossing through function.

How can you stop the envelope of a sinc function crossing the function. I would like it to just skim the maxima points as shown by the drawn envelope in Sinc_envelope.jpg attached.

x = linspace(-20,20,500);

y = abs(sin(x)./(x)).*abs(sin(x)./(x));

[up,lo]=envelope(y,1,'peak');

plot(x,y)

hold on

%plot(x,up)

plot(x,up)

Answer 1

[Akira Agata]

That is due to a characteristics of interpolation method (Spline) used in the envelope function. How about detecting peaks and interpolate them by "Shape-preserving piecewise cubic" ? The following is an example.

x = linspace(-20,20,500);
y = abs(sin(x)./(x)).*abs(sin(x)./(x));

[pk,loc] = findpeaks(y,x);
y2 = interp1(loc,pk,x,'pchip');

plot(x,y)
hold on
plot(x,y2)
legend({'Original','Envelope'},'FontSize',14)