Johnston Filters and Optimal SNR in Maximally Decimated Filter Banks

Abstract

In the design of maximally decimated filter banks, conventional practice is to use Johnston filters at both the analysis and synthesis ends. This paper proposes a two-step procedure: First, select suitable Johnston filters for the analysis side for good coding of the input; then design the synthesis filters to optimize the signal to reconstructed noise ratio SNR. A detailed example shows that one can do somewhat better than Johnston filters at the synthesis end. 1 Introduction This paper concerns the maximally decimated filter bank in Figure 1. The analysis filters are typically frequency selective: H 0 lowpass and H 1 highpass. Such systems are used in subband coding and decoding of speech, images, and video for transmission and storage. Subband coders have been adopted in many new international coding standards [1]. Even though the analysis and synthesis filters are linear time-invariant (LTI), the overall system is in general a linear periodically time-varying (LPTV) system because..