Subband merging in cosine-modulated filter banks

Recently, a new method for constructing nonuniform modulated lapped transforms (MLTs) was introduced, by combining subband filters of a uniform MLT. The design, however, was restricted to combining two or four subband filters only, and no systematic design procedure was given. In this letter, we propose an extension to the above-mentioned method that allows arbitrary numbers of subbands to be combined in a systematic way. We investigate the general case of combining filters in arbitrary cosine-modulated filter banks, and give conditions on how to combine the constituent filters such that the resulting nonuniform filter banks have suitable frequency responses.

I. Introduction

Recently, a new method for constructing nonuniform modulated lapped transforms (MLTs) was introduced [1], [2] by combining subband filters of a uniform MLT. We shall refer to this method as subband merging. The combined subband filters have better time localization than the noncombined filters at the expense of a decrease in frequency localization. Since the nonuniform filter banks are obtained by simply taking linear combinations of the filters of a uniform MLT, the proposed method allows for an efficient implementation of time-varying transforms without the need for transition filters. It was shown that subband merging can be used beneficially for reducing ringing artifacts, e.g., reverberation and pre-echo, in audio and speech coding [2]. The design of such transforms, however, was restricted to combining two or four subband filters only, and no systematic design procedure was given.