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Is there a term to describe this IIR averaging/smoothing filter?

$ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $

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  • $\begingroup$ it should be noted that $$ 0 < \alpha \le 1 $$ for the leaky integrator to appear most like an integrator, then $$ 0 < \alpha \ll 1 $$ this is the integrator to undo the differentiator of DC blocking filter. i like to represent it in terms of the single pole value which is $$p = 1-\alpha$$ so $$ y[n] \ = \ p \, y[n-1] + (1-p) x[n] $$ and the transfer function is $$ H(z) \triangleq \frac{Y(z)}{X(z)} = \frac{(1-p)z}{z-p} $$ $\endgroup$ Sep 21 '17 at 23:54
  • $\begingroup$ also maybe related: dsp.stackexchange.com/questions/4699/… $\endgroup$
    – user13267
    Sep 22 '17 at 1:37
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This is often called a leaky integrator, a special case of a first-order IIR lowpass filter. They are discussed in more detail in several previous questions:

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It is called an exponentially weighted moving average (EWMA) filter. Here is a previous answer where I provided a Matlab script for computing $\alpha$ for a desired cutoff frequency: Exponential moving average cut-off frequency

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  • $\begingroup$ i think Andy is correct. $\endgroup$ Sep 21 '17 at 23:41
  • $\begingroup$ I'm not gone on using Moving Average for describing an Autoregressive filter, though I've certainly heard the term before. $\endgroup$
    – Peter K.
    Sep 22 '17 at 0:42
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Wikipedia calls it "basic exponential smoothing".

I'd call it a first order smoother or first order lowpass filter.

Some combination of those words will probably work.

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  • $\begingroup$ sounds to me to be a Wikipedia neologism. but i dunno. i guess it implies a DC gain of 0 dB, which is important. $\endgroup$ Sep 21 '17 at 23:42
  • $\begingroup$ @robertbristow-johnson not so sure about the "basic" but I'd seen it called exponential smoothing or an exponential filter before Wikipedia existed :) $\endgroup$
    – hobbs
    Sep 22 '17 at 4:55

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