What indices of the original sequence are retained in the output of the decimate function?

I am using the decimate function y = decimate(x,r) and I need to know to which index in x the value y(i) corresponds.

This is not explicitly addressed in the documentation. In the first example the number of points is k*r+1 and according to the code it seems y(1) corresponds to index 1 in x, while and y(length(y)) correponds to index length(x) in x.

In the second example of the documentation, where length(x) is not of the form k*r+1, it seems y(length(y)) corresponds to the last index of the original vector x.

Is that always the case? Would that depend on the type of filter applied (e.g. Chebyshev vs FIR) ?

Thanks for any input on the matter.

Regards.

G. Garcia

For convenience, here is the second example of the documentation:

r = 13;
n = 16:365;
lx = length(n);
x = sin(2*pi*n/153) + cos(2*pi*n/127);

plot(0:lx-1,x,'o')
hold on
y = decimate(x,r,5);
stem(lx-1:-r:0,fliplr(y),'ro','filled','markersize',4)

legend('Original','Decimated','Location','south')
xlabel('Sample number')
ylabel('Signal')

And the associated graph, showing correspondance between last element of x and last element of y:

Answer 1

[Voss]

From item #3 in the Algorithms section of the documentation for decimate:

"In the resampled sequence (y), y(end) matches x(end) when the IIR filter is used, and y(1) matches x(1) when the FIR filter is used."

[Gaëtan Garcia]

Thanks for pointing that out. I missed it. That said, nothing is said about the default filter (Chebyshev). Any idea?

I am reluctant to switch to another filter type just to answer this question. Indeed, I am not a specialist of filtering. I am using methods for the identification of the dynamic parameters of robots, and the user specifically uses the Chebyshev filter and gives a reasonable value of the cutting frequency. So I would feel safer sticking to that.

I still accepted your answer since, worst case scenario, I can look into the IIR filter (FIR would cause phase distorsion, which is not acceptable in my application).

Thanks for your input.

[Voss]

By default, decimate uses a lowpass Chebyshev Type I infinite impulse response (IIR) filter of order 8.

[Gaëtan Garcia]

Okay, now I get it. I did not know that the Chebyshev filter was an IIR filter, so I thought the information in the documentation was incomplete. Now to be honest, I should have realized that a filter was either FIR or IIR...

Now I really have all I need. Thank you again for being patient enough to connect the dots...

Regards.

G. Garcia