Simulate polyphase fir filter
The polyphase filter bank
(pfb) uses a 4 times overlap fir filter before the fft. The
filter is 8192*4 points long. 4 points spaced by 8192 are added
together to give the 8k output. The data is then shifted by 8k and the
process is repeated.
The response of sine waves and noise were checked
using the 8192 length hamming filter. Sine waves and noise were
generated on the computer and passed through the filter.
The plots show the pfb
response to dc, sine waves, and noise (.ps) (.pdf):
- Page 1: the coefficients for the 8192, 4 times overlap, hamming
- Top: The coef. read from the file and normalized to 32768.
There are 8192*4=32768 coef. The dashed blue lines show the 4 8192
- Center: Sum over the 4 coef spaced by 8192 points. This shows
the dc gain of the filter for the 8k points. The average dc gain is
- Bottom: The Peak value (sum(abs(4 points)) for each of the 8192
output points. The max Peak gain is 1.0 (the filter was built setting
the pk gain to 1).
- Page 2: sine wave and noise response.
- Top sine wave: 64K points long with 256 cycles. Black in before
the filter, blue is after the filter.
- The amplitude and rms both decreased by about .845.
- Center: noise before the filter. The rms is 10 counts.
- Bottom: noise after the filter. The new rms is 7.52
- the filter decreases the noise rms by .752
- The dcGain for the 8192 hamming filter is .842
- The peak gain is unity.
- Sine wave rms and pk are reduced by .845
- The noise rms is reduced by .752