Page 1: filter for decimate=4,8,16,32, The dcGain is the integral
over each filter divided by the decimation length.
The filter is generated by computing a sinx/x for the requested
decimation length and then multiplying this by the hanning filter.
The filter coeff read from disk have been normalized to 32K
(since they are 16 bit numbers).
Page 2: pushing a sine wave through the filter.
Top: sine wave used as input. It actually extended for 64K
samples.
Bottom: (sine waves)/decimation after filtering. The amplitude
of the sine
wave has decreased by about .625 .
Jeff reports the dc gain of these filters to be about .627 so
the values agree.
Page 3: filtering noise. The input noise had an rms of 10. There
were 64K samples.
Top: noise after filtering and decimating. The bottom (black)
is decimate by 4. The top (blue) is decimate by 32. An offset has been
added for display. There has been no divide by the decimation.
Center: Noise Rms after filtering (with no divide by
decimation). The noise rises as
sqrt(decimation).
Bottom: Noise Rms after filtering/sqrt(decimation). The value
is constant at .61 . This is pretty close to jeffs .627 dc gain.