Ladies, Gentlemen,

Consider following set of moving average filters:

(1) - 100 coefficients equal to 1/100
(2) --- 95 coefficients equal to 1/95
(3) --- 90 coefficients equal to 1/90
(4) --- 85 coefficients equal to 1/85
(5) --- 80 coefficients equal to 1/80
(6) --- 75 coefficients equal to 1/75
(7) --- 70 coefficients equal to 1/70
(8) --- 65 coefficients equal to 1/65
(9) --- 60 coefficients equal to 1/60
(10) - 55 coefficients equal to 1/55

Suppose filters are implemented in sequence. What are ripple and attenuation of the whole set of filters?

Responding to Mr Commentator I define ripple 1 dB, cut off band 1 tone (1/6 of octave) and attenuation as little as possible.


  • $\begingroup$ You have to define ripple and attenuation in order to answer this question. The resulting filter is no standard frequency-selective filter, so it's not immediately clear how these parameters should be defined. $\endgroup$
    – Matt L.
    Dec 29, 2015 at 20:14

1 Answer 1


George Theodosiou: As Matt L. said, your final filter is not a standard filter having, say, a visible passband with some measureable passband ripple. For example, the combined frequency magnitude response of just your first three moving average filters implemented one after the other (what we call "cascaded filters") is the following:

enter image description here

The value of 0.1 on the horizontal axis is equivalent to 0.1 times the filter's input data sample rate measured in Hz.

What we can say is: The combined frequency response of multiple filters implemented one after the other is the product of all the filters' complex-valued frequency responses.

  • $\begingroup$ My dear Teacher, let me express my gratitude for your detailed answer. What I understand is that these cascaded filters do not work. Regards $\endgroup$ Dec 30, 2015 at 16:26

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