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

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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:

採用された回答

Voss
Voss 2022 年 11 月 29 日
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."
  3 件のコメント
Gaëtan Garcia
Gaëtan Garcia 2022 年 11 月 29 日
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

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