## Notes on Low-Pass Filter Coefficients

September 28, 2004

Jeff Mock

The file lpf_coefficients.txt, which is
created automatically as part of the filter generator's output, contains
the actual values of the low-pass filter coefficients. The values are all
real numbers converted from the fixed-point value used in hardware, which
results in the quantizing effect of the bit length. Taking a DFT of these
coefficients will give a more realistic jagged noise floor.

The file contains a few comments about the filter in lines beginning with
a "#". The bit width of the coefficients, the decimation of the filter,
width of the filter and such are stored here. The current filter has a
width of 24 and a decimation of 14, so there are 14*24=336 lines of filter
coefficients in the rest of the file.

It is a symmetric even filter so the first 168 values are the same
as the last 168 values in reverse order.

In the hardware, the gain of the filter is scaled by the "gain" comment at
the beginning of the file (about 1.05) to accommodate for the window
function and the truncated *sin(x)/x* to give a mean gain of 1.0 for
the filter. This scaling is not built into the coefficients and is done
after the filter.