One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

Vector quantization

During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts

Separable Karhunen Loeve transforms for the weighted universal transform coding algorithm

The weighted universal transform code (WUTC) is a two-stage transform code that replaces JPEG's single, non-optimal transform code with a jointly designed collection of transform codes to achieve good performance across a broader class of possible sources. Unfortunately, the performance gains of WUTC are achieved at the expense of significant increases in computational complexity and larger codes. We here present a faster, more space-efficient WUTC algorithm. The new algorithm uses separable coding instead of direct KLT. While separable coding gives performance comparable to that of WUTC, it uses only 1/8 of the floating-point multiplications and 1/32 of storage of direct KLT. Experimental results included in this work compare the performance of new separable WUTC with both the WUTC and other fast variations of that algorithm