An algebraic approach to discrete short-time Fourier transform analysis and synthesis (original) (raw)

Design of filters for discrete short-time Fourier transform synthesis

ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1985

In this paper we present a nethod f or computing the synthesis filter (window) needed in a weighted overlap-add (WOLA) scheme for the reconstruction of signals in analysis/synthesis systems used to implement the discrete short time Fourier transform (DSTFT). The method is based on an algebraic representation of the analysis synthesis process and assume that the analysis filter (window) is known, that its length N is larger than or equal to the transform size (i.e. the numbe± of frequency bands) M, that no modification of the DSTFT is performed, and that exact signal reconstruction (unity system) is to be achieved. The last condition can be achieved only if the shift R of the sliding analysis window satisfies 1 < R < H.

Input and/or Output Pruning of Composite Length FFTs Using a DIF-DIT Transform Decomposition

IEEE Transactions on Signal Processing, 2009

Pruned fast Fourier transforms (FFTs) can be efficient alternatives to compute DFTs when the input vector is zero padded and/or several output elements are not required. In this correspondence, a new method to prune composite length FFTs is proposed. The proposed pruning method uses decimation in frequency (DIF) and decimation in time (DIT) to decompose a DFT into stages of smaller DFTs. The pruning process is carried out on the input stage and the output stage of the decomposed transform. The proposed pruning method is flexible since it can perform input and/or output pruning over any composite length FFT, action that no other pruning method reported in the literature can carry out. Additionally, no restriction exists with the number of consecutive inputs and consecutive outputs that can be used. Finally, it is shown that the proposed pruning method generates efficient pruned power-of-three and power-of-two length FFTs.

IMPLEMENTATION OF A FLEXIBLE AND SYNTHESIZABLE FFT PROCESSOR

The Fast Fourier Transform (FFT) is one of the rudimentary operations in field of digital signal and image processing. Some of the very vital applications of the fast Fourier transform include Signal analysis, Sound filtering, Data compression, Partial differential equations, Multiplication of large integers, Image filtering etc. Fast Fourier transform (FFT) is an efficient implementation of the discrete Fourier transform (DFT). This paper concentrates on the development of the Fast Fourier Transform (FFT), based on Decimation-In- Time (DIT) domain, Radix-2 algorithm, this paper uses VERILOG as a design entity. The input of Fast Fourier transform has been given by a keyboard using a test bench and output has been displayed using the waveforms on the Xilinx Design Suite 10.1 and Modelsim 6.4b and synthesis results in Xilinx show that the computation for calculating the 32-point Fast Fourier transform is efficient in terms of speed.

Efficient FFT algorithm based on the DST

International Conference on Acoustics, Speech, and Signal Processing

The N-point DFT of a real sequence can be implemented via the real (cos.DFT) and imaginary (ShDFT) components. The N-point cos.DFT in Eurn can be developed from N/Z-point cos, DFT and N/4-point discrete sine transform (DST) . Similarly the N-point sin.DFT can be developed from N/Z-point sin.DFT and NI4-point DST. Using this approach an efficient algorithm (involving real arithmetic only) for an N-point DFT is -.

A Comparative Study on Discrete Fourier Transformation for Digital Signal Analysis

2019

In this article, the basic information on discrete signals, discrete Fourier series, discrete Fourier transformation and their computational implement of signal processing system are described. Now a day, digital signal processing (DSP) is an important research topic because it significantly increases the overall value of hearing protection. From millions of signals, DSP suppresses noise without blocking the speech signal easily. Again without compromising communication, DSP systems protect the users from unhealthy noise exposure. This study addressed some mathematical and graphical techniques for discrete signals reconstruction by using Discrete Fourier Transformation (DFT). DFT is one of the most popular analyzed techniques for DSP system. In this work, we will try to separate the input signal into the real and imaginary part by using DFT algorithm in MATLAB. On the other hand, we will try to reconstruct the given discrete signal with the help of MATLAB program with graphical representation. 1. Introduction Now a day, signal reconstruction from partial Fourier domain information has been interesting to a number of different authors both for particular applications and for its inherent theoretical value [1]. Previous work in this area has involved developing conditions under which signals are uniquely specified with Fourier transform magnitude or phase [2] or signed magnitude information and developing practical algorithms for recovering signals from this information. In this paper, we consider the problem of reconstructing signals from only discrete Fourier transform (or inverse discrete Fourier transform) sign information [3]. By interpolated DFT method with maximum sidelobe decay windows, a multi-frequency signal was analyzed [4]. Again, to improve the accuracy of periodic signal analysis another algorithm was performed [5]. This proposed approach required quite modest additional computational burden which make it suitable for real-time signal professing. Firstly, they showed that how the proposed method can be used in the case of DFT analysis of harmonic signals, and secondly, it was considered that the digital wattmeter application area in electrical power-system measurement. To analyze the exponential signal by the interpolated DFT algorithm another method was described [6]. In [7], DFT algorithm analyzed in low-cost power quality measurement systems based on a DSP processor.

BFT—Low-Latency Bit-Slice Design of Discrete Fourier Transform

Journal of Low Power Electronics and Applications

Structures for the evaluation of fast Fourier transforms are important components in several signal-processing applications and communication systems. Their capabilities play a key role in the performance enhancement of the whole system in which they are embedded. In this paper, a novel implementation of the discrete Fourier transform is proposed, based on a bit-slice approach and on the exploitation of the input sequence finite word length. Input samples of the sequence to be transformed are split into binary sequences and each one is Fourier transformed using only complex sums. An FPGA-based solution characterized by low latency and low power consumption is designed. Simulations have been carried out, first in the Matlab environment, then emulated in Quartus IDE with Intel. The hardware implementation of the conceived system and the test for the functional accuracy verification have been performed, adopting the DE2-115 development board from Terasic, which is equipped with the Cyc...

A Review on Reconfigurable Fourier and Fermat Transforms for Software Radios.

International Journal of Engineering Sciences & Research Technology, 2014

Reconfiguration is an essential part of Software Radio (SR) technology. The systems are designed for change in operating mode with the aim to carry out several types of computations. In this SR context, the Fast Fourier Transform (FFT) operator is defined as a common operator for many classical telecommunications operations. It reviews a new architecture for this operator that makes it a device intended to perform two different transforms. The first one is the Fast Fourier Transform (FFT) used for the classical operations in the complex field. The second one is the Fermat Number Transform (FNT) used for the finite operations in the Galois Field (GF). This operator can be reconfigured to switch from an operator dedicated to compute the FFT in the complex field to an operator which computes the FNT in the Galois Field.

Simplified Bluestein Numerical Fast Fourier Transforms Algorithm For Dsp And Asp

2017

This research was designed to develop a simplified Bluestein numerical FFT algorithm necessary for the processing of digital signals. The simplified numerical algorithm developed in this study is abbreviated with SBNADSP. The methodology adopted in this work was iterative and incremental development design. The major technology used in this work is the Bluestein numerical FFT algorithm. The study set the pace for its goal by re-indexing, decomposing, and simplifying the default Fast Fourier Transform Algorithms (the Bluestein FFT Algorithm). The improved efficiency of the Bluestein FFT algorithm is accounted for by the obvious reduction in the number of operations and operators in the simplified Bluestein algorithms. The SBTNADSP is designed to have four products, and three exponentiations against the default Bluestein FFT algorithm which has six exponentiations and eight products. Since the increase in the number of operators increases the length of operation, it is therefore reaso...