re: Exponential Moving Average - Frequency Response

["Byron Lord" <horribilicus@xxxxxxxxxxxxxxx>]

"carrslem"  <carrslem@xxxxxxx> wrote:
  $
  $ Can anyone provide me a math expression
  $ which describes the frequency response
  $ of an exp MA?
  $     Carroll Slemaker

There's a good book called "Understanding Digital
Signal Processing" by Lyons.  At Amazon it is
this hyperlink:
   <http://www.amazon.com/exec/obidos/tg/detail/-
/0201634678/> 

They sell it used for US$40.00.

Lyons discusses exponential moving averages in
section 8.5 on pages 341-348.  He presents the
transfer function in equation (8-26).  It is
"the frequency response" in complex variables:

H(w) = numer / denom
numer = alpha
denom = 1 - (cos(w)*(1-alpha)) + (j*sin(w)*(1-
alpha))

where w = frequency in radians  (lowercase omega)
where j = sqrt(-1)

The transfer function is PERIODIC, because this
is a sampled-data system.

I would imagine you are most interested in the
magnitude of the transfer function, which is
just sqrt( (realpart^2) + (imagpart^2) ).