The Line Spectral Frequency Model of a Finite-Length Sequence

作者：Yedlapalli Satya Sudhakar^*; Hari K V S

来源：IEEE Journal of Selected Topics in Signal Processing, 2010, 4(3): 646-658.

DOI：10.1109/JSTSP.2010.2048233

• Annihilating (AH) sequence
• antisymmetric
• fixed-point approximation
• Levinson-Durbin
• line spectral frequency (LSF)
• line spectral pair (LSP)
• linear prediction
• linear phase
• minimum phase
• normalized phase
• roots of a polynomial
• spectral decomposition
• symmetric

The line spectral frequency (LSF) of a causal finite length sequence is a frequency at which the spectrum of the sequence annihilates or the magnitude spectrum has a spectral null. A causal finite-length sequence with (L + 1) samples having exactly L-LSFs, is referred as an Annihilating (AH) sequence. Using some spectral properties of finite-length sequences, and some model parameters, we develop spectral decomposition structures, which are used to translate any finite-length sequence to an equivalent set of AH-sequences defined by LSFs and some complex constants. This alternate representation format of any finite-length sequence is referred as its LSF-Model. For a finite-length sequence, one can obtain multiple LSF-Models by varying the model parameters. The LSF-Model, in time domain can be used to synthesize any arbitrary causal finite-length sequence in terms of its characteristic AH-sequences. In the frequency domain, the LSF-Model can be used to obtain the spectral samples of the sequence as a linear combination of spectra of its characteristic AH-sequences. We also summarize the utility of the LSF-Model in practical discrete signal processing systems.

• 出版日期2010-6