Multidimensional Digital Signal Processing Research Articles

Minimizing write operation for multi-dimensional DSP applications via a two-level partition technique with complete memory latency hiding

Most scientific and digital signal processing (DSP) applications are recursive or iterative. The execution of these applications on a chip multiprocessor (CMP) encounters two challenges. First, as most of the digital signal processing applications are both computation intensive and data intensive, an inefficient scheduling scheme may generate huge amount of write operation, cost a lot of time, and consume significant amount of energy. Second, because CPU speed has been increased dramatically compared with memory speed, the slowness of memory hinders the overall system performance. In this paper, we develop a Two-Level Partition (TLP) algorithm that can minimize write operation while achieving full parallelism for multi-dimensional DSP applications running on CMPs which employ scratchpad memory (SPM) as on-chip memory (e.g., the IBM Cell processor). Experiments on DSP benchmarks demonstrate the effectiveness and efficiency of the TLP algorithm, namely, the TLP algorithm can completely hide memory latencies to achieve full parallelism and generate the least amount of write operation to main memory compared with previous approaches. Experimental results show that our proposed algorithm is superior to all known methods, including the list scheduling, rotation scheduling, Partition Scheduling with Prefetching (PSP), and Iterational Retiming with Partitioning (IRP) algorithms. Furthermore, the TLP scheduling algorithm can reduce write operation to main memory by 45.35% and reduce the schedule length by 23.7% on average compared with the IRP scheduling algorithm, the best known algorithm.

Complex Hadamard transform of digital signals: properties and applications

In this paper, we present a class of Complex Hadamard matrices, which are constructed on the base of well–known real Hadamard construction algorithm. The general properties of the developed matrices are discussed and algorithms for reordering and fast calculation of spectral coefficients are given. On the basis of theoretical investigations two applications of complex Hadamard transformation in the area of multidimensional digital signal processing are given. A new method for audio watermarking in the phase spectrum of audio signals and new method for spectrum optimisation of truncated orthogonal transforms are presented. The obtained result lead to the conclusion, that the elaborated complex Hadamard transform can be used efficiently in digital signal processing for spectral analysis, pattern recognition, digital watermarking, transformation, coding and transmission of one–dimensional and two–dimensional signals.

On exploring inter-iteration parallelism within rate-balanced multirate multidimensional DSP algorithms

Although the notion of the parallelism in multidimensional applications has existed for a long time, it is so far unknown what the bound (if any) of inter-iteration parallelism in multirate multidimensional digital signal processing (DSP) algorithms is, and whether the maximum inter-iteration parallelism can be achieved for arbitrary multirate data flow algorithms. This paper explores the bound of inter-iteration parallelism within rate-balanced multirate multidimensional DSP algorithms and proves that this parallelism can always be achieved in hardware system given the availability of a large number of processors and the interconnections between them.

Multidimensional synchronous dataflow

Signal flow graphs with dataflow semantics have been used in signal processing system simulation, algorithm development, and real-time system design. Dataflow semantics implicitly expose function parallelism by imposing only a partial ordering constraint on the execution of functions. One particular form of dataflow called synchronous dataflow (SDF) has been quite popular in programming environments for digital signal processing (DSP) since it has strong formal properties and is ideally suited for expressing multirate DSP algorithms. However, SDF and other dataflow models use first-in first-out (FIFO) queues on the communication channels and are thus ideally suited only for one-dimensional (1-D) signal processing algorithms. While multidimensional systems can also be expressed by collapsing arrays into 1-D streams, such modeling is often awkward and can obscure potential data parallelism that might be present. SDF can be generalized to multiple dimensions; this model is called multidimensional synchronous dataflow (MDSDF). This paper presents MDSDF and shows how MDSDF can be efficiently used to model a variety of multidimensional DSP systems, as well as other types of systems that are not modeled elegantly in SDF. However, MDSDF generalizes the FIFO queues used in SDF to arrays and, thus, is capable only of expressing systems sampled on rectangular lattices. This paper also presents a generalization of MDSDF that is capable of handling arbitrary sampling lattices and lattice-changing operations such as nonrectangular decimation and interpolation. An example of a practical system is given to show the usefulness of this model. The key challenge in generalizing the MDSDF model is preserving static schedulability, which eliminates the overhead associated with dynamic scheduling, and preserving a model where data parallelism, as well as functional parallelism, is fully explicit.

Minimization of memory access overhead for multidimensional DSP applications via multilevel partitioning and scheduling

Massive uniform nested loops are broadly used in multidimensional digital signal processing (DSP) applications. Due to the large amount of data handled by such applications, the optimization of data accesses by fully utilizing the local memory and minimizing communication overhead is important in order to improve the overall system performance. Most of the traditional partition strategies do not consider the effect of data access on the computational performance. In this paper, a multilevel partitioning method, based on a static data scheduling technique known as carrot-hole data scheduling, is proposed to control the data traffic between different levels of memory. Based on this data schedule, optimal partition vector, scheduling vector and the partition size are chosen in such a way to minimize communication overhead. Nonhomogeneous size partitions are the final result of the partition scheme which produces a significant performance improvement. Experiments show that by using this technique, local memory misses are significantly reduced as compared to results obtained from traditional methods. This method can be used in application specific DSP system design and compiler for DSP processors.

Optimal data scheduling for uniform multidimensional applications

Uniform nested loops are broadly used in scientific and multidimensional digital signal processing applications. Due to the amount of data handled by such applications, on-chip memory is required to improve the data access and overall system performance. In this study a static data scheduling method, carrot-hole data scheduling, is proposed for multidimensional applications, in order to control the data traffic between different levels of memory. Based on this data schedule, optimal partitioning and scheduling are selected. Experiments show that by using this technique, on-chip memory misses are significantly reduced as compared to results obtained from traditional methods. The carrot-hole data scheduling method is proven to obtain smallest on-chip memory misses compared with other linear scheduling and partitioning schemes.

Efficient solution of block linear systems with Toeplitz entries using a channel decomposition technique

Abstract This paper is concerned with the development of efficient solvers for block linear systems with Toeplitz entries. Fast block Toeplitz solvers are required in a wide range of applications in the area of multichannel and multidimensional digital signal processing. The presentation and the derivation of all algorithms proposed in this paper are based on the context of multichannel FIR Wiener filtering. A novel channel decomposition technique is applied to obtain fast, order recursive algorithms that require scalar operations, only. The proposed algorithms can accommodate multichannel filter of different filter orders and manage to get free of matrix operations. Two basic algorithm structures are derived, the Levinson type and the Schur type. They are both based on suitable permutations that unravel the recursive nature of the pertinent matrices and enable the development of fast block linear system solvers. Normalized versions are also derived and a simple test for detecting the positive definiteness of a block matrix with Toeplitz entries, is obtained. An efficient lattice structure, that requires scalar operations, is also derived and is subsequently used to obtain Schur-type recursions. The Schur-type algorithm admits full parallelism and, if parallel processing environment is available, it reduces processing time by an order of magnitude. To illustrate the structure of the proposed algorithms, Matlab code is provided for the fast Levinson-type algorithm, as well as for the Schur counterpart.

Multidimensional digital signal processing: problems, progress, and future scopes

Some of the key mathematical limitations encountered in multidimensional digital signal processing research, the useful general settings in which various topical investigations are facilitated, and directions for future research are summarized. The discussion covers multidimensional sampling, multidimensional signal processing over polydisc algebra, nonlinear multidimensional filtering and prediction, and nonlinear nonstationary multidimensional modelling approaches.

Discretization and solution of elliptic PDEs-a digital signal processing approach

A digital signal processing (DSP) approach is used to study numerical methods for discretizing and solving linear elliptic partial differential equations (PDEs). Whereas conventional PDE analysis techniques rely on matrix analysis and on a space-domain point of view to study the performance of solution methods, the DSP approach described here relies on frequency-domain analysis and on multidimensional DSP techniques. Both discretization schemes and solution methods are discussed. In the area of discretization, mode-dependent finite-difference schemes for general second-order elliptic PDEs are examined, and are illustrated by considering the Poisson, Helmholtz, and convection-diffusion equations as examples. In the area of solution methods, the authors focus on methods applicable to self-adjoint positive definite elliptic PDEs. Both direct and iterative methods are discussed, including fast Poisson solvers, elementary and accelerated relaxation methods, multigrid methods, preconditioned conjugate gradient methods and domain-decomposition techniques. In addition to describing these methods in a DSP setting, an up-to-date survey of recent developments is also provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Discrete radon transform

This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure. This observation allows construction of fast direct and inverse transforms. Moreover, we show that the DRT can be used to compute various generalizations of the classical Radon transform (RT) and, in particular, the generalization where straight lines are replaced by curves and weight functions are introduced into the integrals along these curves. In fact, we describe not a single transform, but a class of transforms, representatives of which correspond in one way or another to discrete versions of the RT and its generalizations. An interesting observation is that the exact inversion algorithm cannot be obtained directly from Radon's inversion formula. Given the fact that the RT has no nontrivial one-dimensional analog, exact invertibility makes the DRT a useful tool geared specifically for multidimensional digital signal processing. Exact invertibility of the DRT, flexibility in its definition, and fast computational algorithm affect present applications and open possibilities for new ones. Some of these applications are discussed in the paper.

Study of the computational complexity of algorithms in multidimensional digital signal processing

Study of the computational complexity of algorithms in multidimensional digital signal processing