Efficient implementation of discrete Pascal transform using difference operators

An alternative way is provided to define the discrete Pascal transform using difference operators to reveal the fundamental concept of the transform, in both one- and two-dimensional cases, which is extended to cover non-square two-dimensional applications. Efficient modularised implementations are proposed.

Digital signal processing and digital system design using discrete cosine transform [student course]

The discrete cosine transform (DCT) is an important functional block for image processing applications. The implementation of a DCT has been viewed as a specialized research task. We apply a micro-architecture based methodology to the hardware implementation of an efficient DCT algorithm in a digital design course. Several circuit optimization and design space exploration techniques at the register-transfer and logic levels are introduced in class for generating the final design. The students not only learn how the algorithm can be implemented, but also receive insights about how other signal processing algorithms can be translated into a hardware implementation. Since signal processing has very broad applications, the study and implementation of an extensively used signal processing algorithm in a digital design course significantly enhances the learning experience in both digital signal processing and digital design areas for the students.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Shift, scaling and derivative properties for the discrete cosine transform

A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

VLSI design and implementation of 2-D Inverse Discrete Wavelet Transform

This paper proposes a JPEG-2000 compliant architecture capable of computing the 2 -D Inverse Discrete Wavelet Transform. The proposed architecture uses a single processor and a row-based schedule to minimize control and routing complexity and to ensure that processor utilization is kept at 100%. The design incorporates the handling of borders through the use of symmetric extension. The architecture has been implemented on the Xilinx Virtex2 FPGA.

Multiresolution analysis (discrete wavelet transform) through Daubechies family for emotion recognition in speech

We propose a study of the mathematical properties of voice as an audio signal -- This work includes signals in which the channel conditions are not ideal for emotion recognition -- Multiresolution analysis- discrete wavelet transform – was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states -- ANNs proved to be a system that allows an appropriate classification of such states -- This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features -- Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify

Nonuniform Depth Distribution Selection with Discrete Fourier Transform

info:eu-repo/semantics/inPress

Development of a New Transform:MRT

Fourier transform methods are employed heavily in digital signal processing. Discrete Fourier Transform (DFT) is among the most commonly used digital signal transforms. The exponential kernel of the DFT has the properties of symmetry and periodicity. Fast Fourier Transform (FFT) methods for fast DFT computation exploit these kernel properties in different ways. In this thesis, an approach of grouping data on the basis of the corresponding phase of the exponential kernel of the DFT is exploited to introduce a new digital signal transform, named the M-dimensional Real Transform (MRT), for l-D and 2-D signals. The new transform is developed using number theoretic principles as regards its specific features. A few properties of the transform are explored, and an inverse transform presented. A fundamental assumption is that the size of the input signal be even. The transform computation involves only real additions. The MRT is an integer-to-integer transform. There are two kinds of redundancy, complete redundancy & derived redundancy, in MRT. Redundancy is analyzed and removed to arrive at a more compact version called the Unique MRT (UMRT). l-D UMRT is a non-expansive transform for all signal sizes, while the 2-D UMRT is non-expansive for signal sizes that are powers of 2. The 2-D UMRT is applied in image processing applications like image compression and orientation analysis. The MRT & UMRT, being general transforms, will find potential applications in various fields of signal and image processing.

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms

This work compares and contrasts results of classifying time-domain ECG signals with pathological conditions taken from the MITBIH arrhythmia database. Linear discriminant analysis and a multi-layer perceptron were used as classifiers. The neural network was trained by two different methods, namely back-propagation and a genetic algorithm. Converting the time-domain signal into the wavelet domain reduced the dimensionality of the problem at least 10-fold. This was achieved using wavelets from the db6 family as well as using adaptive wavelets generated using two different strategies. The wavelet transforms used in this study were limited to two decomposition levels. A neural network with evolved weights proved to be the best classifier with a maximum of 99.6% accuracy when optimised wavelet-transform ECG data wits presented to its input and 95.9% accuracy when the signals presented to its input were decomposed using db6 wavelets. The linear discriminant analysis achieved a maximum classification accuracy of 95.7% when presented with optimised and 95.5% with db6 wavelet coefficients. It is shown that the much simpler signal representation of a few wavelet coefficients obtained through an optimised discrete wavelet transform facilitates the classification of non-stationary time-variant signals task considerably. In addition, the results indicate that wavelet optimisation may improve the classification ability of a neural network. (c) 2005 Elsevier B.V. All rights reserved.

A note on a practical relationship between filter coefficients and scaling and wavelet functions of Discrete Wavelet Transforms

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement the wavelet theory, that is well documented in the literature, being important for researchers who work with this tool for time-frequency analysis. (c) 2011 Elsevier Ltd. All rights reserved.

Wavelets in a problem of signal processing

In this work a new method is proposed for noise reduction in speech signals in the wavelet domain. The method for signal processing makes use of a transfer function, obtained as a polynomial combination of three processings, denominated operators. The proposed method has the objective of overcoming the deficiencies of the thresholding methods and the effective processing of speech corrupted by real noises. Using the method, two speech signals are processed, contaminated by white noise and colored noises. To verify the quality of the processed signals, two evaluation measures are used: signal to noise ratio (SNR) and perceptual evaluation of speech quality (PESQ).

Parallel-recusive filter structures for the computation of discrete transforms

A general approach is presented for implementing discrete transforms as a set of first-order or second-order recursive digital filters. Clenshaw's recurrence formulae are used to formulate the second-order filters. The resulting structure is suitable for efficient implementation of discrete transforms in VLSI or FPGA circuits. The general approach is applied to the discrete Legendre transform as an illustration.

Accelerating FPGA-based evolution of wavelet transform filters by optimized task scheduling

Adaptive embedded systems are required in various applications. This work addresses these needs in the area of adaptive image compression in FPGA devices. A simplified version of an evolution strategy is utilized to optimize wavelet filters of a Discrete Wavelet Transform algorithm. We propose an adaptive image compression system in FPGA where optimized memory architecture, parallel processing and optimized task scheduling allow reducing the time of evolution. The proposed solution has been extensively evaluated in terms of the quality of compression as well as the processing time. The proposed architecture reduces the time of evolution by 44% compared to our previous reports while maintaining the quality of compression unchanged with respect to existing implementations. The system is able to find an optimized set of wavelet filters in less than 2 min whenever the input type of data changes.