Extended Lapped Transform Research Articles

Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks

The recently introduced exponentially modulated filter bank (EMFB) is a -channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR) property if the prototype filter of an -channel PR cosine modulated filter bank (CMFB) is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT) type of implementation solutions are studied. The ELT-based EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs) when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems.

Algorithm-based low-power transform coding architectures: the multirate approach

In most low-power VLSI designs, the supply voltage is usually reduced to lower the total power consumption. However, the device speed will be degraded as the supply voltage goes down. In this paper, we propose new algorithmic-level techniques to compensate the increased delays based on the multirate approach. We apply the technique of polyphase decomposition to design low-power transform coding architectures, in which the transform coefficients are computed through decimated low-speed input sequences. Since the operating frequency is M-times slower than the original design while the system throughput rate is still maintained, the speed penalty can be compensated at the architectural level. We start with the design of low-power multirate discrete cosine transform (DCT)/inverse discrete cosine transform (IDCT) VLSI architectures. Then the multirate low-power design is extended to the modulated lapped transform (MLT), extended lapped transform (ELT), and a unified low-power transform coding architecture. Finally, we perform finite-precision analysis for the multirate DCT architectures. The analytical results can help us to choose the optimal wordlength for each DCT channel under required signal-to-noise ratio (SNR) constraint, which can further reduce the power consumption at the circuit level. The proposed multirate architectures can also be applied to very high-speed block discrete transforms in which only low-speed operators are required.

Time-varying lapped transforms and wavelet packets

The perfect reconstruction conditions for a time-varying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is developed employing a time varying, tree association of ELTs. In all cases perfect reconstruction is inherently assured.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Extended lapped transforms: properties, applications, and fast algorithms

The family of lapped orthogonal transforms is extended to include basis functions of arbitrary length. Within this new family, the extended lapped transform (ELT) is introduced, as a generalization of the previously reported modulated lapped transform (MLT). Design techniques and fast algorithms for the ELT are presented, as well as examples that demonstrate the good performance of the ELT in signal coding applications. Therefore, the ELT is a promising substitute for traditional block transforms in transform coding systems, and also a good substitute for less efficient filter banks in subband coding systems. >

Fast wavelet transforms based on the extended lapped transform

A new family of wavelet transforms (WTs) based on the extended lapped transform (ELT) is introduced. A new optimisation criterion for the ELT butterfly angles is presented, leading to ELT-based WTs with virtually the same performance but a much lower computational complexity than the standard maximally-regular WTs.