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Practical filter banks use realizable (nonideal) analysis/synthesis filters with finite support and finite stopband attenuation. After critical decimation, such nonideal responses inevitably produce aliasing. This chapter shows how perfect reconstruction (PR) is nevertheless achievable by alias cancellation at the synthesis stage, even when individual subband filters are far from brick-wall responses. We derive the classic two-channel PR conditions, generalize with the polyphase matrix formulation for N-channel banks, and connect to block-transform implementations (Discrete Fourier Transform—DFT/ Modified Discrete Cosine Transform—-MDCT) that achieve PR by construction.

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Filter Banks with Nonideal Filters

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  • 发表日期：

    2026年

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  • Gerald Schuller

摘要

Practical filter banks use realizable (nonideal) analysis/synthesis filters with finite support and finite stopband attenuation. After critical decimation, such nonideal responses inevitably produce aliasing. This chapter shows how perfect reconstruction (PR) is nevertheless achievable by alias cancellation at the synthesis stage, even when individual subband filters are far from brick-wall responses. We derive the classic two-channel PR conditions, generalize with the polyphase matrix formulation for N-channel banks, and connect to block-transform implementations (Discrete Fourier Transform—DFT/ Modified Discrete Cosine Transform—-MDCT) that achieve PR by construction.