Simulate polyphase fir filter

11oct07

        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 filter.

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 sections.
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 .842.
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

Conclusions:

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

processing: x101/070926/pfbSim.pro

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