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Line Spectral Frequencies The Line Spectrum Pairs or Line Spectrum Frequencies (LSP's or LSF's) are a way of representing the coefficients of an all-pole filter. They are widely used in speech coding and analysis because they have good properties for quantization and error protection. This page contains two papers describing novel algorithms related to LSF's: (1) a very efficient way to convert the LSF polynomials with complex roots into equivalent polynomials with only real roots, and (2) a novel rootfinding algorithm which guarantees convergence for these types of polynomials. Taken together, these two papers provide a simple and efficient way to convert filter coefficients to the LSF representation.

The In-Place, In-Order Prime Factor FFT. While most common Fast Fourier Transform algorithms that use power-of-2 sizes, other sizes may be useful in specific applications. In particular, the Prime Factor Algorithm (PFA) can be used for transform sizes that are the product of multiple small integers. Dr. Burrus was one of the first to recognize that the PFA can be structured in such a way that (1) both the input and output data arrays are in natural order, and (2) the computations can be done in-place, so that the transformed data replaces the input data in memory. However, his original approach required the offline computation of of several indexing tables, so it was difficult to use. This paper describes an elegant way of integrating this indexing into the algorithm, making it easy to implement it for multiple transform sizes.

Polyphase filtering. This paper describes a way to implement a bank of bandpass filters, to split a signal into multiple narrowband components. The advantage of this structure was that it allowed efficient computation of the band outputs, and allowed the bands to be recombined to recover the original signal. This paper is referenced in some descriptions of the filter banks used in MPEG audio encoding and decoding. It is mainly of historical interest, as much additional work on Perfect Reconstruction filter banks has been done since it's publication.

Other publications and patents are available on myown1.com and rothweiler.us.

$Date: 2016/02/16 12:29:24 $