Showing papers on "Discrete sine transform published in 2016"

Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels

Abstract: In this manuscript we propose the discrete versions for the recently introduced fractional derivatives with nonsingular Mittag-Leffler function. The properties of such fractional differences are studied and the discrete integration by parts formulas are proved. Then a discrete variational problem is considered with an illustrative example. Finally, some more tools for these derivatives and their discrete versions have been obtained.

Amplitude-preserving nonlinear adaptive multiple attenuation using the high-order sparse Radon transform

Abstract: The Radon transform is widely used for multiple elimination. Since the Radon transform is not an orthogonal transform, it cannot preserve the amplitude of primary reflections well. The prediction and adaptive subtraction method is another widely used approach for multiple attenuation, which demands that the primaries are orthogonal with the multiples. However, the orthogonality assumption is not true for non-stationary field seismic data. In this paper, the high-order sparse Radon transform (HOSRT) method is introduced to protect the amplitude variation with offset information during the multiple subtraction procedures. The HOSRT incorporates the high-resolution Radon transform with the orthogonal polynomial transform. Because the Radon transform contains the trajectory information of seismic events and the orthogonal polynomial transform contains the amplitude variation information of seismic events, their combination constructs an overcomplete transform and obtains the benefits of both the high-resolution property of the Radon transform and the amplitude preservation of the orthogonal polynomial transform. A fast nonlinear filter is adopted in the adaptive subtraction step in order to avoid the orthogonality assumption that is used in traditional adaptive subtraction methods. The application of the proposed approach to synthetic and field data examples shows that the proposed method can improve the separation performance by preserving more useful energy.

Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT

Abstract: The nonlinear Fourier transform represents a signal in terms of its continuous spectrum, discrete eigenvalues, and the corresponding discrete spectral amplitudes. This paper presents a new bi-directional algorithm for computing the discrete spectral amplitudes, which addresses the significant problem of rounding errors inherent in previously known techniques. We use the proposed method to obtain accurate spectral-domain noise statistics for 2-soliton signals using numerical simulation.

Fast Discrete Linear Canonical Transform Based on CM-CC-CM Decomposition and FFT

Abstract: In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and without oversampling operation is developed. This DLCT is based on the well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp multiplications (CMs) and one discrete chirp convolution (CC). This decomposition doesn’t use any scaling operation which will change the sampling period or cause the interpolation error. Compared with previous works, DLCT calculated by direct summation and DLCT based on center discrete dilated Hermite functions (CDDHFs), the proposed method implemented by FFTs has much lower computational complexity. The relation between the proposed DLCT and the continuous LCT is also derived to approximate the samples of the continuous LCT. Simulation results show that the proposed method somewhat outperforms the CDDHFs-based method in the approximation accuracy. Besides, the proposed method has approximate additivity property with error as small as the CDDHFs-based method. Most importantly, the proposed method has perfect reversibility, which doesn’t hold in many existing DLCTs. With this property, it is unnecessary to develop the inverse DLCT additionally because it can be replaced by the forward DLCT.

Discrete Fourier Transform Method for Discrimination of Digital Scintillation Pulses in Mixed Neutron-Gamma Fields

Abstract: A discrete Fourier transform method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain using the sine and cosine Fourier transforms in combination with the discrete Fourier transform. The method is largely benefited from considerable differences that usually is available between the zero-frequency components of sine and cosine and the norm of the amplitude of the DFT for neutrons and gamma-ray signals. Moreover, working in frequency domain naturally results in considerable suppression of the unwanted effects of various noise sources that is expected to be effective in time domain methods. The proposed method could also be assumed as a generalized nonlinear weighting method that could result in a new class of pulse shape discrimination methods, beyond definition of the DFT. A comparison to the traditional charge integration method (CIM), as well as the frequency gradient analysis method (FGAM) and the wavelet packet transform method (WPTM) has been presented to demonstrate the applicability and efficiency of the method for real-world applications. The method, in general, shows better discrimination Figure of Merits (FoMs) at both the low-light outputs and in average over the studied energy domain. A noise analysis has been performed for all of the abovementioned methods. It reveals that the frequency domain methods (FGAM and DFTM) are less sensitive to the noise effects.

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Abstract: Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.

An efficient implementation of fourth-order compact finite difference scheme for Poisson equation with Dirichlet boundary conditions

Abstract: Fourth-order compact finite difference scheme has been proposed for solving the Poisson equation with Dirichlet boundary conditions for some time. An efficient implementation of such numerical scheme is often desired for practical usage. In this paper, based on fast discrete Sine transform, we design an efficient algorithm to implement this scheme. To do this, Poisson equation is first discretized by fourth-order compact finite difference method. The subsequent discretized system is not solved by the usual method-matrix inversion, instead it is solved with the fast discrete Sine transform. By doing this way, the computational cost of proposed algorithm for such scheme with large grid numbers can be greatly reduced. Detailed numerical algorithm of this fast solver for one-dimensional, two-dimensional and three dimensional Poisson equation has been presented. Numerical results in one dimension, two dimensions, three dimensions and four dimensions have shown that the applied compact finite difference scheme has fourth order accuracy and can be efficiently implemented.

The Nonuniform Discrete Fourier Transform And Its Applications In Signal Processing

Abstract: Thank you very much for downloading the nonuniform discrete fourier transform and its applications in signal processing. Maybe you have knowledge that, people have search hundreds times for their favorite books like this the nonuniform discrete fourier transform and its applications in signal processing, but end up in malicious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some infectious virus inside their computer.

Fourier Pairs of Discrete Support with Little Structure

Abstract: We give a simple proof of the fact, first proved in a stronger form in Lev and Olevskii (Quasicrystals with discrete support and spectrum, arXiv preprint arXiv:1501.00085 , 2014), that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson Summation Formula finitely many times. More specifically the support of both the measure and its Fourier Transform are not contained in a finite union of arithmetic progressions.

Optical spectrum encryption in associated fractional Fourier transform and gyrator transform domain

Abstract: An optical spectrum encryption algorithm for hyperspectral image is proposed in this paper, in which the spatial and spectrum information can be encrypted simultaneously. The Baker mapping is utilized to scramble each band of the hyperspectral cube before the optical transform. Subsequently, 100 bands are divided into real part and imaginary part of the complex function expressing light field. Then, the scrambled data is imported into fractional Fourier transform and gyrator transform system. A random binary vector is designed and employed in the optical transform for enhancing the security of the encryption system. The amplitude and phase information in the output plane can be regarded as the encrypted information. Some numerical simulations are made to demonstrate the performance of the proposed encryption system.

Computer-Aided Diagnosis System for Alzheimer's Disease Using Different Discrete Transform Techniques.

Abstract: The different discrete transform techniques such as discrete cosine transform (DCT), discrete sine transform (DST), discrete wavelet transform (DWT), and mel-scale frequency cepstral coefficients (MFCCs) are powerful feature extraction techniques. This article presents a proposed computer-aided diagnosis (CAD) system for extracting the most effective and significant features of Alzheimer’s disease (AD) using these different discrete transform techniques and MFCC techniques. Linear support vector machine has been used as a classifier in this article. Experimental results conclude that the proposed CAD system using MFCC technique for AD recognition has a great improvement for the system performance with small number of significant extracted features, as compared with the CAD system based on DCT, DST, DWT, and the hybrid combination methods of the different transform techniques.

Discrete Hirota equation: discrete Darboux transformation and new discrete soliton solutions

Abstract: Under investigation in this paper is the discrete Hirota equation which is a combination of discrete NLS and discrete complex modified KdV equations. The discrete spectral problem analysis has been made, and discrete Darboux transformation(DT) has been constructed based on \(2\times 2\) discrete Lax pair for system (1.3). In addition, we have derived new discrete one-soliton solutions by using the obtained discrete DT for system (1.3). Figures have been plotted to display the dynamic features of discrete solitons.

Partial discrete fourier transform-spread in an orthogonal frequency division multiplexing system

Abstract: A method of transmitting data may include converting a stream of serial data bits into a set of parallel quadrature amplitude modulation (QAM) symbols. The method may additionally include applying a partial discrete Fourier transform-spread technique to transform a block of low-frequency subcarriers into a single-carrier QAM signal. The single-carrier QAM signal may bear information of a first subset of QAM symbols from the set of parallel QAM symbols. The method may additionally include transforming one or more remaining QAM symbols to form one or more subcarriers. Each of the one or more subcarriers may bear information of a corresponding QAM symbol from the one or more remaining QAM symbols. The method may additionally include generating a hybrid signal that includes the single-carrier QAM signal and the one or more subcarriers. The method may additionally include transmitting the hybrid signal.

A Switch-Based Interpolated DFT for the Small Number of Acquired Sine Wave Cycles

Abstract: The frequency of a real sinusoid is often estimated by interpolated discrete Fourier transform (IpDFT) algorithms because of the high accuracy and low computational burden. However, conventional IpDFTs focus on frequency estimation when the number of acquired sine wave cycles (NASC) is more than two. Frequency estimation with the small NASC is applicable in manufacturing processes, radar level measurement, and other applications. The spectral leakage of the negative frequency (the image component) significantly distorts the positive frequency when the NASC is small, dramatically degrading estimation accuracy. In particular, it is a challenging task for existing IpDFTs to provide high estimation accuracy when the NASC is less than one. In this paper, a switch-based IpDFT is proposed to provide high frequency estimation accuracy for $\text {NASC} . The theoretical variance of the algorithm in white Gaussian noise is formulated, which includes the upper bound and the lower bound. Computer simulations and real measurements are conducted to corroborate the theoretical analysis and to demonstrate that the proposed algorithm achieves better accuracy and antinoise capability for $\text {NASC} than existing algorithms.

Uncertainty principles for discrete signals associated with the fractional Fourier and linear canonical transforms

Abstract: The fractional Fourier transform (FRFT), which generalizes the classical Fourier transform, has gained much popularity in recent years because of its applications in many areas, including optics, radar, and signal processing. There are relations between duration in time and bandwidth in fractional frequency for analog signals, which are called the uncertainty principles of the FRFT. However, these relations are only suitable for analog signals and have not been investigated in discrete signals. In practice, an analog signal is usually represented by its discrete samples. The purpose of this paper is to propose an equivalent uncertainty principle for the FRFT in discrete signals. First, we define the time spread and the fractional frequency spread for discrete signals. Then, we derive an uncertainty relation between these two spreads. The derived results are also extended to the linear canonical transform, which is a generalized form of the FRFT.

Optimal Discrete Gaussian Function: The Closed-Form Functions Satisfying Tao’s and Donoho’s Uncertainty Principle With Nyquist Bandwidth

Abstract: In this paper, closed-form discrete Gaussian functions are proposed. The first property of these functions is that their discrete Fourier transforms are still discrete Gaussian functions with different index parameter. This index parameter, which is an analogy to the variance in continuous Gaussian functions, controls the width of the function shape. Second, the discrete Gaussian functions are positive and bell-shaped. More important, they also have finite support and consecutive zeros. Thus, they satisfy Tao’s and Donoho’s uncertainty principle of discrete signal. The construction of these discrete Gaussian functions is inspired by Kong’s zeroth-order discrete Hermite Gaussian functions. Three examples are discussed.

The Pascal Triangle (1654), the Reed-Muller-Fourier Transform (1992), and the Discrete Pascal Transform (2005)

Abstract: This paper makes a theoretical comparative analysis of the Reed-Muller-Fourier Transform, Pascal matrices based on the Pascal triangle, and the Discrete Pascal Transform. The Reed-Muller-Fourier Transform was not originated by a Pascal matrix, however it happens to show a strong family resemblance with it, sharing several basic properties. Its area of application is the multiple-valued switching theory, mainly to obtain polynomial expressions from the value vector of multiple-valued functions. The Discrete Pascal Transform was introduced over a decade later, based on an ad hoc modification of a Pascal matrix, for applications on picture processing. It is however shown that a Discrete Pascal Transform of size p, taken modulo p equals the special Reed-Muller-Fourier Transform for the same p and n = 1. The Sierpinski fractal is close related to the Pascal matrix. Data structures based on the Sierpinski triangle have been successfully used to solve special problems in switching theory. Some of them will be addressed in the paper.

Integer Cosine Transforms for High-Efficiency Image and Video Coding

Abstract: Matrix methods for constructing one-norm order-8 and -16 integer cosine transforms are considered. One-norm order-8 and -16 integer transforms are proposed and fast algorithms are developed that implement these transforms with a low computational complexity that is less by a factor of 3---5 than the complexity of well-known algorithms and is less by a factor of 10 than that in the H.265 standard.

An adaptive recursive discrete fourier transform technique for the reference current generation of single-phase shunt active power filters

Abstract: This paper proposes a novel adaptive recursive discrete Fourier transform (ARDFT) technique for the reference current generation of single-phase shunt active power filters (APFs). The suggested method is robust to input frequency changes and exactly extracts the reference current of the APF. Modeling of the converter system and design procedure of the control parameters are presented in this paper. To confirm the theoretical results, simulation results are provided. These results show effectiveness and excellent performance of the suggested technique.

Interpolation using wavelet transform and discrete cosine transform for high resolution display

Abstract: We propose a new interpolation method based on the hybrid technique combining the discrete wavelet transform (DWT) and discrete cosine transform (DCT). The high frequency wavelet coefficients are interpolated using the zero pad method in the DCT domain. The upscaled image is generated using inverse DWT of interpolated coefficients and original image.

2-D left-Side quaternion discrete fourier transform: Fast algorithm

Abstract: We describe a fast algorithm for the 2-D left-side QDFT which is based on the concept of the tensor representation when the color or four-componnrnt quaternion image is described by a set of 1-D quaternion signals and the 1-D left-side QDFTs over these signals determine values of the 2-D left-side QDFT at corresponding subset of frequency-points. The efficiency of the tensor algorithm for calculating the fast left-side 2-D QDFT is described and compared with the existent methods.  The proposed algorithm of the 2r×2r-point 2-D QDFT uses 18N2 less multiplications than the well-known methods: • column-row method • method of symplectic decomposition.  The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.  The method of quaternion image tensor representation is uique in a sense that it can be used for both left-sida and right-side 2-D QDFTs. 3 Inroduction – Quanterions in Imaging  The quaternion can be considered 4-dimensional generation of a complex number with one real part and three imaginary parts. Any quaternion may be represented in a hyper-complex form Q = a + bi + cj + dk = a + (bi + cj + dk), where a, b, c, and d are real numbers and i, j, and k are three imaginary units with the following multiplication laws: ij = −ji = k, jk = −kj = i, ki = −ik = −j, i2 = j2 = k2 = ijk = −1.  The commutativity does not hold in quaternion algebra, i.e., Q1Q2≠Q2Q1.  A unit pure quaternion is μ=iμi+jμj+kμk such that |μ| = 1, μ 2 = −1 For instance, the number μ=(i+j+k)/√3, μ=(i+j)/√2, and μ=(i-k)/√2  The exponential number is defined as exp(μx) = cos(x) + μ sin(x) = cos(x) + iμi sin(x) +jμj sin(x) +kμk sin(x) 4 RGB Model for Color Images 5  A discrete color image fn,m in the RGB color space can be transformed into imaginary part of quaternion numbers form by encoding the red, green, and blue components of the RGB value as a pure quaternion (with zero real part): fn,m = 0 + (rn,mi + gn,mj + bn,mk) Figure 1: RBG color cube in quaternion space.  The advantage of using quaternion based operations to manipulate color information in an image is that we do not have to process each color channel independently, but rather, treat each color triple as a whole unit. Calculation of the left-side 1-D QDFT  Let fn =(an,bn,cn,dn)=an +ibn +jcn +kdn be the quaternion signal of length N. The left-side 1-D quaternion DFT ( LS QDFT) is defined as 6 If we denote the N-point LS 1-D DFTs of the parts an, bn, cn, and dn of the quaternion signal fn by Ap, Bp, Cp, and Dp, respectively, we can calculate of the LS 1-D QDFT as If the real part is zero, an =0, and fn =(0,bn,cn,dn)=an +ibn +jcn +kdn , the number of operations of multiplication and addition can be estimated as Multiplications and Additions for the left-side 1-D QDFT  In the general case of the quaternion signal fn, the number of operations of multiplication and addition for LS 1-D QDFT can be estimated as 7 The number of operations for the left-side 1-D QDFT can be estimated as Here, we consider that for the fast N-point discrete paired transform-based FFT, the estimation for multiplications and additions are and two 1-D DFTs with real inputs can be calculated by one DFT with complex input, (1) Number of multiplications: Special case 8 The number of operations of multiplication and addition equal or 8N operations of real multiplication less than in (1). The direct and inverse left-side 2-D QDFTs  Given color-in-quaternion image fn,m =an,m +ibn,m +jcn,m +kdn,m , we consider the concept of the left-side 2-D QDFT in the following form: 9 1. Column-row algorithm: The calculation of the separable 2-D N×N-point QDFT by formula 2. The calculation the LS 2-D QDFT by the symplectic decomposition of the color image requires 2N N-point LS 1-D QDFTs. Each of the 1-D QDFT requires two N-point LS 1-D DFTs. Therefore, the column-row method uses 4N N-point LS 1-D DFTs and multiplications or The inverse left-side 2-D QDFT is: Example: N×N-point left-side 2-D QDFT 10 Figure 2. (a) The color image of size 1223×1223 and (b) the 2-D left-side quaternion discrete Fourier transform of the color-inqiuaternion image (in absolute scale and cyclically shifted to the middle). Tensor Representation of the regular 2-D DFT Let fn,m be the gray-scale image of size N×N.  The tensor representation of the image fn,m is the 2D-frequency-and-1D-time representation when the image is described by a set of 1-D splitting-signals each of length N 11 The components of the signals are the ray-sums of the image along the parallel lines Each splitting-signals defines 2-D DFT at N frequency-points of the set on the cartesian lattice Example: Tensor Representation of the 2-D DFT 1-D splitting-signal of the tensor represntation of the image 512×512 12 Figure 3. (a) The Miki-Anoush-Mini image, (b) splitting-signal for the frequency-point (4,1), (c) magnitude of the shifted to the middle 1-D DFT of the signal, and (d) the 2D DFT of the image with the frequency-points of the set T4,1. Tensor Representation of the left-side 2-D QDFT Let fn,m =an,m +ibn,m +jcn,m +kdn,m be the quaternion image of size N×N, (an,m =0). In the tensor representation, the quaternion image is represented by a set of 1-D quaternion splitting-signals each of length N and generated by a set of frequencies (p,s), 13 The components of the signals are defined as Here, the subsets Property of the TT: Example: Tensor Representation of the 2-D LS QDFT The splitting-signal of the tensor represntation of the color image 1223×1223: 14 Figure 5. The 123-point left-side DFT of the (1,4) quaternion splitting-signal; (a) the real part and (b) the i-component of the signal. Figure 4. Color image and (a,b,c) components of the splitting-signal generated by (1,4). Example: Tensor Representation of the 2-D LS QDFT 15 Figure 7. (a) The real part and (b) the imaginary part of the left-side 2-D QDFT of the 2-D color-in-quaternion `girl Anoush\" image. Figure 6. (a) The 1-D left-side QDFT the quaternion splitting-signal f1,4,t (in absolute scale), and (b) the location of 1223 frequency-points of the set T1,4 on the Cartesian grid, wherein this 1-D LS QDFT equals the 2-D LS QDFT of the quaternion image. μ=(i+2j+k)/√6 Tensor Transform: Direction Quaternion Image Components Color image can be reconstructed by its 1-D quaternion splitting-signals or direction color image components defined by 16 Statement 1: The discrete quaternion image of size N×N, where N is prime, can be composed from its (N+1) quaternion direction images or splitting-signals as Color-or-Quaternion Image is The Sum of Direction Image Components 17 Figure 8: (a) The color image and direction images generated by (p,s) equal (b) (1,1), (c) (1,2), and (d) (1,4). The Paired Image Representation: Splitting-Signals and Direction Quaternion Image Components The tensor transform, or representation is redndant for the case N×N, where N is a power of 2. Therefore the tensor transform is modified and new1-D quaternion splitting-signals or direction color image components are calculated by 18 Statement 2: The discrete quaternion image of size N×N, where N=2r, r>1, can be composed from its (3N−2) quaternion direction images as Here JʹN,N is a set of generators (p,s). Such representation of the quaternion image is called the paired transform; it is unitary and therefore not redundant.

A New Data Extrapolation Approach Based on Spectral Partitioning

Abstract: In this letter, we propose a new linear predictive (LP) data extrapolation approach. It involves partitioning the spectrum into multiple spectral subbands and using a different autoregressive (AR) process to model each subband. The new extrapolation approach is then combined with the classical discrete Fourier transform (DFT) to produce a new hybrid LP-DFT spectral estimator to address the detection and estimation problem of multiple sinusoids in a discrete data sequence. Simulation results demonstrate the superiority of the proposed hybrid technique over an existing popular hybrid LP-DFT technique, where a single AR process is used to model the entire spectrum of the data sequence.

Accelerating Discrete Fourier Transforms with dot-product engine

Abstract: Discrete Fourier Transforms (DFT) are extremely useful in signal processing. Usually they are computed with the Fast Fourier Transform (FFT) method as it reduces the computing complexity from O(N2) to O(Nlog(N)). However, FFT is still not powerful enough for many real-time tasks which have stringent requirements on throughput, energy efficiency and cost, such as Internet of Things (IoT). In this paper, we present a solution of computing DFT using the dot-product engine (DPE) - a one transistor one memristor (1T1M) crossbar array with hybrid peripheral circuit support. With this solution, the computing complexity is further reduced to a constant O(λ) independent of the input data size, where λ is the timing ratio of one DPE operation comparing to one real multiplication operation in digital systems.

DWT-DCT-SVD based hybrid lossy image compression technique

Abstract: A new hybrid transform coding methodology for lossy image compression that integrates discrete wavelet transform, discrete cosine Transform and singular value decomposition methods is proposed. The proposed system has enhancements in both the compression ratio and the computational time. The results demonstrate the advantages of the proposed system in comparison to the previous discrete cosine transform and singular value decomposition systems, Improvements in both compression ratio and computational time have been reported.

Analysis of human radar echo signal using warped discrete fourier transform

Abstract: Use of the warped discrete Fourier transform for the time-frequency analysis of the signal on the audio-output of pulse-Doppler radar is examined in this research. The discrete Fourier transform is calculated in points in z-plane that are equidistantly distributed on the unit circle, while the warped discrete Fourier transform is calculated in points that are unevenly distributed on the unit circle. The time-dependent warped discrete Fourier transform for the analysis of the simulated and measured radar signals from a walking human was applied in this research. The results of the time-frequency analysis of radar signals using this transformation are compared with the spectrogram. The results show that the application of the warped discrete Fourier transformation in the radar signal analysis provides a higher concentration of energy around the central Doppler frequency comparing to the spectrogram.

A Duality Theorem for the Discrete Sine Transform - IV (DST - IV)

Abstract: This paper presents a new property called the Duality Theorem for the Discrete Sine Transform - IV (DST - IV). Discrete Sine Transform - IV is a finite duration discrete transform. This transform is mathematically related to the famous Discrete Fourier Transform (DFT) and is used in Image Processing applications, but it is surprising that it has escaped attention from pure mathematicians. Most of the properties of the Discrete Sine Transform - IV are quite similar to those of the DFT and Discrete Cosine Transform (DCT) although some differences persist. A formal derivation of the Duality Theorem for the Discrete Sine Transform - IV is presented which was hitherto not mentioned or derived in the literature. The Duality Theorem finds application in the computation of the discrete time - domain function from the DST - IV frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and thus results in the saving of computation time and implementation cost significantly. Its usage can be successfully exploited in the arenas of Signal Processing, Image Processing, and Communication Systems, where it is common to encounter cases involving the discrete - time and the discrete frequency signals to have the same aspect or resemblance.

Improving the Goertzel–Blahut Algorithm

Abstract: A novel method for computing the discrete Fourier transform (DFT) over a finite field based on the Goertzel-Blahut algorithm is described. The novel method is currently the best one for computing the DFT over even extensions of the characteristic two finite field, in terms of multiplicative complexity.