Re: Need Ideas!!


"Neelabh" <neelabh2@xxxxxxxxxxx> wrote in message
news:tNOdnf5vs8thhRXanZ2dnUVZ_ryqnZ2d@xxxxxxxxxxxxxxx
I'd be deeply grateful if someone could help me out. I'm looking for ideas
for an academic project on telecommunications DSP. Everything I've looked
at so far has been done several times over. Could someone point out some
topics in the field that I could work on?

Thanks in advance.

Here's one:

The Remez exchange algorithm allows minimax solutions to approximation
problems. Digital filter design is one of the applications. See
Parks-McClellan.

Less well known is that the same algorithm can be used to find minimax
solutions to approximation problems that include equality constraints. See
Temes, Barcilon & Marshall.

The formulation and algorithms for both are pretty straightforward.

On the other hand, the same objectives can be met using linear programming -
where the formulation and amount of computation is relatively larger.

The similarity suggests that there is a relationship between linear
programming and the Remez algorithm and/or the modified Remez algorithm with
equality constraints. Understanding the relationship between the two might
be interesting unto itself and it may provide new insights that suggest new
approaches / algorithms for filter design.

I don't know if the relationship is understood by some or not. I don't
think it's a question that's ever asked - but it may have been.
I don't think it's a trivial pursuit - certainly not when insights gained
lead to new algorithms, etc!

If you want a simpler problem, consider showing how the modified Remez
exchange algorithm can be used (along with a convergence proof) to design
the all-positive "starting point" filter used by Hermann & Schussler in
realizing minimum phase equiripple FIR filters. It goes like this:

- Design a filter with real frequency response with only positive ripples in
the stop band (so all the zeros in the stop band are double zeros).

- Take the "square root" of the filter to yield a minimum phase equiripple
FIR filter with real frequency response. Now the zeros in the stop band are
single zeros and the equiripples are both positive and negative.

It's the first step that really counts.

The method also requires that one juggle the first step design criteria so
that the "square root" filter meets reasonable specifications.

It's probably not the most practical method or most in demand but it is
academic.

Your question implies graduate level work - so I figure you can figure out
easily enough which pertinent papers apply here.

Fred




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