Showing papers on "Discrete sine transform published in 2022"

Digital Image Watermarking Technique Using Discrete Wavelet Transform and Discrete Cosine Transform

Abstract: Digital watermarking has been proposed as a viable solution to the need of copyright protection and authentication of multimedia data in a networked environment, since it makes possible to identify the author, owner, distributor or authorized consumer of a document. In this paper a new watermarking technique to add a code to digital images is presented: the method operates in the frequency domain embedding a pseudo-random sequence of real numbers in a selected set of DCT coefficient. And a new method for digital image watermarking which does not require the original image for watermark detection. The watermark is added in select coefficients with significant image energy in the transform domain in order to ensure non- erasability of the watermark. Advantages of the proposed method include: improved resistance to attacks on the watermark, implicit visual masking utilizing the time-frequency localization property of wavelet transform and a robust definition for the threshold which validates the watermark.. Experimental results demonstrate that this proposed technique is robust to most of the signal processing techniques and geometric distortions.

Comparison of discrete transforms for deep-neural-networks-based speech enhancement

Abstract: In recent studies of speech enhancement, a deep-learning model is trained to predict clean speech spectra from the known noisy spectra of speech. Rather than using the traditional discrete Fourier transform (DFT), this paper considers other well-known transforms to generate the speech spectra for deep-learning-based speech enhancement. In addition to the DFT, seven different transforms were tested: discrete Cosine transform, discrete Sine transform, discrete Haar transform, discrete Hadamard transform, discrete Tchebichef transform, discrete Krawtchouk transform, and discrete Tchebichef-Krawtchouk transform. Two deep-learning architectures were tested: convolutional neural networks (CNN) and fully connected neural networks. Experiments were performed for the NOIZEUS database, and various speech quality and intelligibility measures were adopted for performance evaluation. The quality and intelligibility scores of the enhanced speech demonstrate that discrete Sine transformation is better suited for the front-end processing with a CNN as it outperformed the DFT in this kind of application. The achieved results demonstrate that combining two or more existing transforms could improve the performance in specific conditions. The tested models suggest that we should not assume that the DFT is optimal in front-end processing with deep neural networks (DNNs). On this basis, other discrete transformations should be taken into account when designing robust DNN-based speech processing applications.

An Area-efficient Unified Transform Architecture for VVC

Abstract: The next-generation video coding standard Versatile Video Coding (VVC) adopts Multiple Transform Selection (MTS) to the transform module, improving coding efficiency at the expense of high computational complexity. Compared to High Efficiency Video Coding (HEVC), VVC supports larger sizes and extends the transform types to Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-VII, and DCT-VIII. This paper presents an area-efficient unified architecture for VVC. To reduce the area consumption, we propose an optimized calculation scheme for general transformations where the transform matrix is decomposed into two simpler matrices named the Low-value matrix and the Error matrix. Based on the decomposition algorithm, Shift-Addition Units (SAUs)-based circuits are designed to conduct matrix multiplication and can be reused by three types. As a result, this unified architecture is capable of performing all types and sizes in VVC. The synthesis results indicate that this architecture achieves an area reduction of 37.9% $\sim$ 72.2% compared with related works for 32-point transforms.

Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures

Abstract: The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals. In this article, we introduce the notion of discrete quadratic-phase Fourier transform, which encompasses a wider class of discrete Fourier transforms, including classical discrete Fourier transform, discrete fractional Fourier transform, discrete linear canonical transform, discrete Fresnal transform, and so on. To begin with, we examine the fundamental aspects of the discrete quadratic-phase Fourier transform, including the formulation of Parseval’s and reconstruction formulae. To extend the scope of the present study, we establish weighted and non-weighted convolution and correlation structures associated with the discrete quadratic-phase Fourier transform.

A graph signal processing approach to Fourier-like number-theoretic transforms

Abstract: In this paper, we employ a graph signal processing approach to redefine Fourier-like number-theoretic transforms, which includes the Fourier number transform itself, the Hartley number transform and specific types of the cosine number transform and the sine number transform. Our strategy basically consists in identifying graphs whose Laplacian or adjacency matrix has an eigenbasis coinciding with the basis employed to define each of the aforementioned transforms. We then demonstrate how to extend this idea to multidimensional cases and provide a general definition, which corresponds to the graph Fourier number transform (GFNT). We develop illustrative examples and perform a preliminary investigation regarding the use of the GFNT in an image encryption scenario.

Complex-Conjugate Symmetry of Coefficients of Two-Dimensional Discrete Fourier Transform with Variable Parameters of Real Signals

Abstract: Methods and algorithms for digital one-dimensional and two-dimensional Fourier processing have the widest applications in solving a wide range of practical problems in many areas of scientific research. The paper gives a generalization of standard discrete Fourier transform in the form of parametric discrete Fourier transform, and considers the theory of its application. The article considers new discrete two-dimensional Fourier transform which is discrete two-dimensional Fourier transform with variable parameters, which, being a generalization of standard two-dimensional discrete Fourier transform, has a number of advantages over the standard one. Due to the widespread use of real signals in practice, the paper investigates the properties of the complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for this class of signals. The concept of cross-complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for real signals is introduced. The properties of the cross-complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for real signals are confirmed by the results of mathematical modeling. Methods and algorithms for fast computation of discrete Fourier transform with variable parameters of real signals for various combinations of variable parameters have been developed.

Sine Fourier Transform-based Frequency Estimation

Abstract: This paper presents an approach for frequency estimation based on applying a sine Fourier transform and observations of particularly selected characteristic points of sidelobes. The bias of frequency estimation caused by the refusal to complement the developed algorithm by a corresponding cosine transform is eliminated by a specific selection of frequencies, for which a Fourier transform is calculated, and consecutive iteration of calculations is done for various durations of the analyzed signal. This paper also presents approaches for the recognition of a frequency interval with the exact value of frequency for a case of an analyzed signal with noise contamination.

Analysis of the Effects of Orthogonal Transformation Techniques on Channel Equalizers Used in OFDM

Abstract: In this study, it is proposed to combine fast Walsh Hadamard transform (FWHT) with orthogonal transforms such as discrete cosine transform (DCT) and discrete sine transform (DST) to increase the performance of time domain (TDE) and frequency domain channel equalizers (FDE) used in OFDM systems. In order to test the performance of the proposed FWHT FFT/DCT/DST-OFDM waveforms with TDE and FDE, numerical simulation studies are carried out in the frequency selective Rayleigh fading channel environment. From the obtained numerical results, it is understood that the proposed FWHT FFT/DCT/DST OFDM-TDE systems have approximately 8 dB better bit error rate (BER) performance than FWHT FFT/DCT/DST OFDM-FDE methods.

Piece-Wise Fourier Transform of Aperiodic Functions

Abstract: One new step-by-step procedure to obtain Fourier transform of some aperiodic waveshapes, without using Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) and window functions, is presented in this paper. Waveshapes are approximated by multi-peaked analytically extended function (MP-AEF) which is a piece-wise function. The main advantage of this procedure is that it can handle signals with sharp peaks, as opposite to other Fourier transform procedures, which makes it suitable for lightning currents' waveshapes. The procedure is confirmed on single-wave cosine, triangular, trapezoidal, and double-exponential waveshapes. The advantage of this procedure is that it provides Fourier transform for any chosen time interval of observation as well as for infinite time duration signals.

Directional Analytic Discrete Cosine Frames

Abstract: Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

The Discrete Fourier Transform

Abstract: AbstractIn this chapter, the discrete Fourier transform and its inverse are derived using the orthogonality property of harmonically related discrete sinusoidal or complex exponential waveforms. This version is the only one of the four versions of Fourier analysis in which the variables in both the time-domain and frequency-domain are discrete and finite. The finite extent signal is periodically extended and represented by a finite set of harmonically related discrete sinusoidal or complex exponential waveforms. The difference between time-domain and frequency-domain representations is pointed out. A brief view of the Fourier analysis is given. Properties of the DFT are presented. Some applications of the DFT are described.KeywordsSinusoidsComplex exponentialsOrthogonalityDiscrete Fourier transformInverse discrete Fourier transformConvolutionInterpolationDecimation

On the perfomance of Hirschman Optimal Transform for Reduction of PAPR in UFMC

Abstract: Abstract Universal filtered multi carrier (UFMC) system is considered to be the best choice for 5G waveform when compared with orthogonal frequency division multiplexing (OFDM), filtered OFDM (f-OFDM), filter bank multi carrier (FBMC) and generalized FDM (GFDM) in terms of spectral leakage, complexity and compatibility with 5G. The all multi carrier systems are suffers from high peak to average power ratio (PAPR) causes non linear functioning in receiver. In this paper, we proposed a Hirschman optimal transform (HOT) based pre-coding for reducing the PAPR in UFMC systems. Results reveals that HOT pre-coded UFMC promising less PAPR compared with discrete cosine transform (DCT), discrete Hartley transform (DHT) and discrete sine transform (DST) and discrete Fourier transform (DFT).

Compexity bound for discrete modelling of quantum Fourier transform

Abstract: A discrete model of a quantum mechanical system with N basis states defined using 2(N-1) parameters. It is shown that the estimate of the complexity of discrete modeling quantum Fourier transform based on the presented model has O(N) order of operations on the specified parameters.

Inverse Transform Using Linearity for Video Coding

Abstract: In hybrid block-based video coding, transform plays an important role in energy compaction. Transform coding converts residual data in the spatial domain into frequency domain data, thereby concentrating energy in a lower frequency band. In VVC (versatile video coding), the primary transform is performed using DCT-II (discrete cosine transform type 2), DST-VII (discrete sine transform type 7), and DCT-VIII (discrete cosine transform type 8). Considering that DCT-II, DST-VII, and DCT-VIII are all linear transforms, inverse transform is proposed to reduce the number of computations by using the linearity of transform. When the proposed inverse transform using linearity is applied to the VVC encoder and decoder, run-time savings can be achieved without decreasing the coding performance relative to the VVC decoder. It is shown that, under VVC common-test conditions (CTC), average decoding time savings values of 4% and 10% are achieved for all intra (AI) and random access (RA) configurations, respectively.

Contrast Enhancement of Gray Image Using Discrete Cosine Transform

Abstract: In this paper a new method for contrast enhancement based on the discrete cosine transform is discussed and implemented. The technique converts the image into DCT domain and the DCT coefficients are modified using proposed mask then the enhanced image is reconstructed using inverse DCT. The discrete cosine transform outperforms with better image quality and with highest PSNR value.

Quantitative phase measurements using 2-D discrete cosine transform in Hilbert phase microscopy

Abstract: Abstract Discrete cosine transform (DCT) is closely related to discrete Fourier transform. This is a separable linear conversion. It can be said that DCT is simpler and faster than DFT as well as FFT. DCT is suitable for extended periodic and symmetric sequences, while DFT is suitable for long periodic sequences. So DCTs are the equivalent of almost double-length DFTs that work on real data with uniform symmetry. Hilbert Phase Microscopy (HPM) is a shot in nature and is a new optical technique for measuring small, high-resolution transverse images associated with clear optical objects. In this paper, we introduce the phase extraction method of a simulated interference scheme with the cosine discrete Fourier transform algorithm in the Hilbert phase microscope.

An Investigation of the Effects of the Transform Techniques in Optical-OFDM Systems

Abstract: In this study, it is proposed to adapt the zero-tail discrete Fourier transform spread OFDM (ZT DFT-s OFDM) waveform to the visible light communication system, which is used as an alternative to OFDM in radio frequency (RF) communication systems. It is aimed to use ZT DCT-s and ZT DST-s OFDM waveforms in optical OFDM systems by replacing conversion techniques such as discrete cosine transform (DCT) and discrete sine transform (DST) with DFT-s block in ZT DFT-s OFDM waveform. Numerical simulation studies are carried out to test the performance of the proposed ZT DCT-s/DFT-s/DST-s optical OFDM waveforms and compare them with other optical OFDM techniques such as ACO-OFDM and DCO-OFDM. From the obtained numerical results, it is understood that the recommended ZT DCT-s, ZT DFT-s and ZT DST-s O-OFDM waveforms, without sacrificing bandwidth, have a better PAPR performance of approximately 2.8 dB than the DCO-OFDM technique and 9.5 dB better than the ACO-OFDM waveform.

A new form of discrete real Fourier transform and its potential applications

Abstract: The paper will present a new version of a real discrete Fourier transform, based on a symmetric frequencies combination of sine and cosine functions. Basic aspects of the construction as well as the potential applications will be discussed. This will include elements of the standard Fourier analysis as well as applications to the class of differential equations in string theory.