Some algebraic aspects of signal processing

✍ Scribed by M. Barnabei; C. Guerrini; L.B. Montefusco

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 756 KB
• Volume: 284
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(98)10131-3

✦ Synopsis

It has recently been shown in (M. Barnabei, L.B. Montefusco, Linear Algebra and applications 274 (1998) 367-388) that the algebraic-combinatorial notion of recursive matrix tan fruitfully be used to represent and easily handle the basic operations of filter theory, such as convolution, up-sampling, and down-sampling. In this Paper we show how the recursive matrix reinterpretation of two-channel FIR filter bank theory leads to a notable simplification in language and proofs, together with an easy and immediate generalization to the M-channel case. For example, in both 2-channel and M-channel cases, perfett reconstruction and alias concelation conditions tan be restated in an algebraic language, thereby obtaining an easy and constructive proof using the fundamental properties of recursive matrices.