Radix‐4 3 based two‐dimensional FFT architecture with efficient data reordering scheme

Multidimensional (MD) discrete Fourier transform (DFT) is a key kernel algorithm in many signal processing applications. In this paper we describe an MD-DFT intellectual property (IP) generator and a bandwidth-efficient MD DFT IP for high performance implementations of 2-D and 3-D DFT on field-programmable gate array (FPGA) platforms. The proposed architecture is generated automatically and is based on a decomposition algorithm that takes into account FPGA resources and the characteristics of off-chip memory access, namely, the burst access pattern of the synchronous dynamic RAM (SDRAM). The IP generator has been integrated into an in-house FPGA development platform, AlgoFLEX, for easy verification and fast integration. The corresponding 2-D and 3-D DFT architectures have been ported onto the BEE3 board and their performance measured and analyzed. The results shows that the architecture can maintain the maximum memory bandwidth throughout the whole procedure while avoiding matrix transpose operations used in most other MD DFT implementations. To further enhance the performance, the proposed architecture is being ported onto the newly released Xilinx ML605 board. The simulation results show that 2 K × 2 K images with complex 64-bit precision can be processed in less than 27 ms.

Multiplication is an important fundamental function in arithmetic operations. Multiplication-based operations such as Multiply and Accumulate(MAC) and inner product are among some of the frequently used computation Intensive Arithmetic Functions(CIAF) currently implemented in many Digital Signal Processing (DSP) applications such as convolution, Fast Fourier Transform(FFT), filtering and in microprocessors m its arithmetic and logic unit. Since multiplication dominates the execution tune of most DSP algorithms, so there is a need of high speed multiplier. Currently, multiplication time is still the dominant factor in determining the instruction cycle time of a DSP chip. The demand for high speed processing has been increasing as a result of expanding computer and signal processing applications. Higher throughput arithmetic operations are important to achieve the desired performance in many real-time signal and image processing applications . One of the key arithmetic operations in such applications is multiplication and the development of fast multiplier circuit has been a subject of interest over decades. Multiplier based on Vedic Mathematics is one of the fast and low power multiplier. Employing this technique in the computation algorithms will reduce the complexity, execution time, power etc. This vedic based multiplier is compared with binary multiplier(partial products method).

An efficient algorithm that places an optimized DG (dependence graph) for 2/sup n/ points of the discrete Fourier transform (DFT) computation is proposed. A one-dimensional DFT is turned into a multidimensional DFT, consisting of a few short DFTs, which is based on the version of the Goertzel algorithm via Horner's rule. The data sequences in the Cooley-Tukey FFT algorithm are in an order that is easily manageable and well suited for vector processors and any parallel machine such as hypercube. >

Discrete Fourier transform (DFT) has many applications in digital signal and image processing and other scientific and technological domains, but its time complexity of direct computation is O(n2), limiting greatly its application range. Thus many people have developed fast Fourier transform (FFT) algorithms, reducing the complexity from O(n2) to O(nlogn)(In this paper logn denotes log2n).But for large n, O(nlogn) is still very high. So multiprocessor systems have been used to speed up the computation of DFT. This paper first introduces a new general method to deduce FFT algorithms, then transforms the deduced second radix-2 decimation-in-time FFT algorithm into another parallelizable sequential form, and finally transforms the latter algorithm into a new parallel FFT algorithm, reducing the time complexity of DFT to O(nlogn/p) (where p is the number of processors). Using similar methods, the authors can also design other new parallel 1-D and 2-D FFT algorithms.

Complex-valued conjugate-symmetric Hadamard transforms ( $\BBC $ -CSHT) are variants of complex Hadamard transforms and found applications in signal processing. In addition, their real-valued transform counterparts ( $\BBR $ -CSHTs) perform comparably with Hadamard transforms (HTs) despite their lower computational complexity. Closed-form factorizations of $\BBC $ -CSHTs and $\BBR $ -CSHTs have recently been proposed to make calculations more efficient. However, there is still room to find effective and general factorizations. This paper presents a simple closed-form complete factorization of $\BBC $ -CSHTs based on that of $\BBR $ -CSHTs. The proposed factorization can be applied to both $\BBC $ - and $\BBR $ -CSHTs with one factorization and it provides several benefits: 1) It can save total implementation costs for both $\BBC $ -CSHTs and $\BBR $ -CSHTs; 2) the generalized $\BBR $ -CSHT factorization significantly reduces its computational cost; 3) memory-saved local orientation detection of images can be achieved; 4) a fast direction-aware transform can be attained; 5) it clarifies that $\BBC $ - and $\BBR $ -CSHTs are closely related to common block transforms, such as the discrete Fourier transform (DFT), binDCT, and HT; and 6) it achieves a new integer complex-valued transform, which can approximate the DFT better than the original $\BBC $ -CSHT. The image orientation estimation and performance in image coding of our $\BBR $ -CSHTs were evaluated through examples of practical applications based on the proposed factorization.

The near field microscopy has been a dynamically developing diagnostic method for the last two decades. The number of measurement modes and data it delivers, sometimes make it difficult for interpreting. Thereby one needs sophisticated methods of extraction to get some specific information from the obtained results. Increasing complexity of the instruments as well as a software allows to acquire several signals simultaneously and to process them in a specific way in order to receive a particular result. Two dimensional Fast Fourier Transformation (2D FFT) is one of the most important tools in the picture analysis in near field microscopy. Such tools as finding specific spatial frequencies or noise filtering are very efficient. In the article we present some results of different modes of AFM measurements, where additional signals were acquired during measurements and by performing 2D FFT with the comparison approach, specific results and information were obtained.

The 16 papers in this special issue focus on adaptive sparse representation of data and applications in signal and image processing.

The complexity of heterogeneous Multi-Processor Systems-on-Chip stretches the limits of software development solutions based on sequential languages such as C/C++. While these are still the most widely used languages in practice, model-based solutions appear to be an efficient alternative. However, the optimized compilation of models for multi-processor systems still presents many open research problems. Among others, static data-flow analyses for models require the adaptation of traditional algorithms used in program analysis (iterative and worklist algorithms). These algorithms operate on Control-Flow Graphs with a unique start node (i.e., a node without predecessors) and assume that every basic block is reachable from this start node.

Discrete Fourier transform (DFT) is a fundamental building block for various signal processing applications, and speeding up large-scale DFT/FFT using distributed processing is often desirable. In this paper, we consider the problem of distributed DFT computation from untrustworthy servers. In particular, we study the scenario where the goal is to compute the DFT of an s-length signal from N distributed and untrustworthy servers, where any l out of N servers can collude. The signal must be kept information-theoretically secure from any l out of N servers. The goal of this paper is to characterize the minimum communication overhead while maintaining security in an information-theoretic sense. The capacity of the secure distributed FFT is defined as the maximum possible ratio of the desired information (signal length s) and the total information received from all N distributed servers. We present lower and upper bounds on capacity of secure distributed FFT, and show that these bounds match exactly when N l is a power of 2, and the bounds match asymptotically when−N becomes large.

Tensor Golub–Kahan method based on Einstein product

FFT is the most compute intensive operation that critically affects the OFDM system performance. In order to support the various OFDM standards, a scalable and reconfigurable FFT architecture is necessary. This paper presents an energy efficient and scalable FFT architecture, which can be dynamically reconfigured to adapt to specifications of different standards. The proposed architecture is based on Radix-43 algorithm and uses a parallel-pipelined unrolled architecture. The proposed architecture can be scaled to support FFTs of sizes up to 64K points. As a proof of concept, FFT architecture for computation of FFTs of sizes 64 to 4K point has been implemented in UMC 65nm 1P10M CMOS process with a maximum clock frequency of 125 MHz and area of 1.05mm2. The power consumption at 40 MHz is 33.5mW for the computation of 4K point FFT. Energy efficiency (FFTs per unit of energy) of the proposed architecture is 1176 for 1K point, 584 for 2K point and 291 for 4K point FFTs at 40 MHz. The proposed architecture shows better performance in terms of scalability and energy efficiency when compared to existing implementations.

The spectral analysis of any signal involves a signal-processing tool using Fourier processors. Chirp Z Transform (CZT) is a modern technique providing ideally any frequency resolution in the spectrum. The conventional filter bank type spectrometer provides low to moderate (few 100 kHz) frequency resolution and if its frequency resolution is to be increased further then the number of channels must be increased to a large extent, necessitating extra hardware and expense. To increase the frequency resolution of a conventional filter bank further, a novel approach using Chirp Z transform has been suggested at low frequency. It is a cost effective and easy to use solution capable of providing both Chirp Z signal processing and Discrete Fourier Transform (DFT) as a special case of CZT. It is an efficient way to perform offline signal processing in applications not requiring real time operation.

A Wavelet Transform (WT) is a mathematical technique that transforms a signal into different frequency components, each analyzed with a resolution that matches its scale. Wavelets are small waves with limited duration and they possess both time and frequency localization, which means they can capture both high-frequency and low-frequency information simultaneously. There are several types of wavelet transforms, and, depending on the application, one may be preferred to the others. For a continuous input signal, the time and scale parameters can be continuous leading to the Continuous Wavelet Transform (CWT) and Discrete wavelets. Image processing is a critical area in modern computing with applications ranging from medical imaging to remote sensing and computer vision. Traditional Fourier analysis has limitations in capturing localized features in images due to its global nature. Wavelet Transform (WT), with its multi-resolution and localized time-frequency representation, provides a powerful alternative for analysing and processing visual information. This paper presents a comprehensive overview of the theory of wavelet transforms, their mathematical foundations, and applications in image processing and signal processing, including compression of images, denoising and feature extraction from images.

An area-delay efficient single-precision floating-point multiplier for VLSI systems

Template matching has many applications in signal processing, image processing, pattern recognition, and video compression. This paper proposes a fast coarse-to-fine template matching algorithm for finding the exact best match, i.e., the match that may be found by a full search. This is obtained by pruning the number of candidates in the full search using the results of a coarse search. Experimental results show that speed ups of a couple of orders of magnitude can easily be achieved using this method for typical low-noise cases of two-dimensional (2-D) template matching.