What is the Laplace transfer function of a moving average? yk=xk+xk−1+xk−2+xk−3+...+xk−N+1N I tried to get it from the z-domain transfer function using conversion tables: ykxk=1+z−1+z−2+z−3+...+z−N+1N
But unless I've read them wrong they don't have the "bricks" I need to get me anywhere.
Answer
ykxk=1+z−1+z−2+z−3+...+z−N+1N
can be re-written as
ykxk=1N1−z−N1−z−1
That should be straightforward to model in the s-domain by replacing z by esT
i.e. H(s)=1N1−e−sTN1−e−sT
This is a SINC function in the frequency domain whose magnitude versus frequency is of the form: sin(πfN)Nsin(πf)
(source)
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