"William E. Sabin" wrote in message
news:6J84f.437250$x96.418250@attbi_s72...

A couple of improvements in the following paragraph:

The filter can be equalized for group delay, as mentioned, with
improvement in the problem. The band edges can be softened, with good
results. A much better way is to use two or more intermediate-performance
filters in cascade. This method softens the edges so that the effect is
greatly reduced. It also improves overall shape factor. A cascade in
this manner of identical bandpass or audio lowpass filters tends in the
limit toward the Bessel or even the Gaussian response. Digital filters
can also use a method called Transition Band Sampling (see Oppenheim and
Schafer 1975)

Delete the incorrect second Reference to Oppenheim and Willsky 1983.

All of these results are related in principle to the Central Limit
Theorem of statistics.

See http://mathworld.wolfram.com/CentralLimitTheorem.html for this
interesting topic. The general idea that the theorem alludes to in this
example is that as sharp-cornered filters are cascaded the passband response
becomes noticeably more rounded at the corners, similar to Bessel and
Gaussian filters.

Smoothing and Windowing methods can be used to reduce sharp corners in
discrete sequences such as digital filters (see Oppenheim and Schafer 1975
and many other sources).

Bill W0IYH