SVD analysis by synthesis of harmonic signals

An analysis by synthesis procedure based on the singular value decomposition (SVD) methodology is proposed. Using this procedure, a criterion for detecting the number of sinusoidal signals in the presence of noise is defined. Consecutive reconstructions are performed, and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal. The number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order. The existence of such a criterion is important for both high-quality reconstruction and spectral analysis. Various spectral estimation techniques used on a reconstructed signal make it possible to retrieve harmonics in a highly noisy environment with very short data lengths     

LSP analysis and processing for speech coders

Linear prediction parameters within CELP coders are commonly represented by line spectral pairs (LSP), giving stable filters and efficient coding. However, LSP manipulation can also alter the frequencies of the represented signals. The authors use computationally efficient LSP manipulation to enhance the intelligibility of speech degraded by acoustic interference     

Comparative analysis of bitplane-based wavelet image coders

Wavelet image encoders based on bitplanes give excellent results in the compression of still images. The bitplane concept has recently been generalised to vectors, and wavelet image encoders based on vector bitplanes have been proposed, some achieving slightly better rate /spl times/ distortion performances than scalar encoders. There remains the open question of whether the use of vector bitplanes has the potential of providing more significant rate /spl times/ distortion improvements over scalar versions. The authors address this question by analysing in detail the performance of adaptations, for the use of vector bitplanes, of four popular wavelet-based bitplane encoders. From this analysis, they determine where the gains in performance of encoders based on vector bitplanes come from. It is concluded that performance improvements may come by increasing the vector dimension, provided that codebooks with good packing properties are used.     

Performance analysis of an ATM multiplexer loaded with VBR trafficgenerated by multimode speech coders

Multimode coders are able to exploit the different characteristics of the speech waveform and to take into account the different peculiarities of background noise, thus allowing improvements in both signal reconstruction and network-offered load. In this context the variable rate code excited linear prediction (VR-CELP) coding, that is, a multimode variable bit rate (VBR) coding based on the CELP technique, has been introduced in the literature and is currently being considered for use in various applications, especially in the third-generation UMTS cellular systems. The target of the paper is to introduce an efficient and accurate framework allowing a network designer to analyze the impact of multimode VBR speech coding on the quality of service (QoS) provided by a wireless/wired ATM network. In order to capture the coder output characteristics, we propose to model a VR-CELP voice source by using a switched batch Bernoulli process (SBBP). More specifically, three models are introduced and compared in terms of accuracy and simplicity in determining network performance. As a result of the comparison, a four-state model has been chosen as the best tradeoff. The model is then used to analytically derive the loss probability and the jitter probability density function of an ATM multiplexer loaded by a number of VR-CELP sources. Finally, the proposed paradigm has been assessed in a case study where we demonstrate that, for a given output ATM link capacity and for a number of telecommunication services involving voice transmission, VR-CELP coding performs better than traditional on-off coding     

IMAGING OF EEG BY SPHERICAL HARMONIC ANALYSIS

A new three dimensional imaging method for electroencephalogram(EEG) is suggested. It consists of the solution of an inward spherical harmonic continuation. The principle of the new method is introduced in Section II, then a few numerical simulation tests are shown and the feasibility of the new method is confirmed by the simulation results.     

Theory of optimal orthonormal subband coders

The theory of the orthogonal transform coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband coders, transform coders, and predictive coders are summarized. Finally, conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands     

Combining speech coders and entropy coders to reduce the bit rate in the compression of speech

The combination of speech coders and entropy coders is investigated, for bit rate reduction. Three speech coders of the celp (code excited linear prediction) type are considered and the residual correlation in lsp (line spectrum pairs) coefficients and gains in a speech frame is exploited. The lossless entropy coders use Huffman, Lzw (lempel ziv welch) and gzip (LZ-Huffrnan) techniques. The greatest efficiency is provided by the adaptive Huffman approach, with a 15 % gain in each type of compressed parameter and an overall average bit rate reduction of 7 % for the FS1016 coder and 5 % for the Tetra and lbc coders.     

Data compression and harmonic analysis

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transform-based image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the information theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the “sampling theorem”, harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future     

Spectrum estimation and harmonic analysis

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.     

Matrix synthesis of harmonic oscillator circuits †

A synthesis method is given for oscillators of the type that may be represented as a single two-port network with a transmission matrix [T]=[A, B;C, D] having its output fed directly back to its input, thereby imposing the condition:

A+D?Δ?1=0,

where ΔΞAD? BC. To obtain sustained oscillation at a single real frequency ω₀ this condition is interpolated at ω₀ by a polynomial equation in s. By identifying the two equations a set of functional values may be obtained for the [T] matrix elements. Four sots of basic circuit are developed in detail from the quadratic or cubic polynomial equation, with Δ = 0 or Δ≠0. Those having Δ = 0 arc well-known forms, but those with Δ =0 are novel.     

An analysis of the efficiency of different SNR-scalable strategies for video coders.

In this paper, we analyze the efficiency of three signal-to-noise scalable strategies for video coders using single-loop motion-compensated prediction (MCP). In our analysis, we assume the video sequences have uniform and constant translational motion and we model MCP as a stochastic filter. We also assume an exponential model for the distortion-rate function of the intraframe coding. The analysis is divided into two parts: the steady-state analysis and the transient analysis. In the first part, only the steady-state response of the coders is taken into account, and, thus, this analysis allows us to asses approximately the efficiency of coders with long input sequences. The transitory analysis considers both the transient and the steady-state responses of the coders, which makes it appropriate to analyze coders using periodic intraframes or with short input sequences. To validate our analysis, theoretical results have been compared to results from encodings of real video sequences using the scalable adaptive motion compensated wavelet video coder. We show that our theoretical analysis effectively describes qualitatively the main trends of every video coding strategy.     

Vlsi solutions for voice and channel coders

In the last few years we have seen a relevant transformation of the telephone network, with an extensive digitalization of the voice transmission and switching able now to reach the subscriber. In the meanwhile various techniques have been implemented to exploit data transmission in an environment designed for voice only. This paper will review this important transformation and its future perspective from the point of view of theic industry by considering several analog/digital basic realization inpcm, analog modem,isdn and radio-communication fields.     

Composite source model of DPCM coders

A new model regarding the difference values of a DPCM coder as a composite source is presented. It can provide a decrease in the entropy of prediction errors and is especially useful in lossless coding and distortion limited compression. Application to image coding demonstrates its effectiveness     

基于FPGA与谐波合成信号发生器的实现

提出一种结合傅里叶级数展开和DDS原理产生任意波形信号发生器的实现方法。利用FPGA设计了15个DDS模块,将一周期正弦波的样值写入DDS模块的ROM表。对目标信号进行傅里叶变换得到信号各次谐波的频率和幅值,取其1~15次谐波的频率作为每个DDS模块的频率控制字,将各个DDS模块输出的样值与输入该模块的频率对应谐波幅值的乘积进行累加,经低通滤波器输出最终所需波形。测试表明,利用该实现方法得到的信号发生器输出波形稳定、频率转换速度快、精度在0.002 79 Hz以内。     

New gain compression factor determination by harmonic analysis insemiconductor lasers

Measurements, on CATV DFB strained QW lasers, of first-order, second-order optical modulation depth (OMD) and, for the first time, of DC component decrease with modulation Δ_DC are fitted within a nonlinear model giving a precise determination of gain compression factor ϵ. This direct determination method at intermediate modulation frequencies is simpler and gives higher precision of ϵ than existing measurement methods such as relaxation resonance peak characteristics or emission wavelength shift     

Construction of optimal subband coders using optimized and optimalquantizers

A method is presented for the optimization of arbitrary quantizers by use of a compensating postfilter. It is shown that the resulting optimized quantizers fit the model of a linear time-invariant filter followed by additive noise uncorrelated with the input which also characterizes the optimal (Lloyd-Max) quantizers. On the basis of this model, an expression for the variance of the error of a subband coder using optimized quantizers is explicitly determined. Given analysis filters which statistically separate the subbands, it is shown that this variance is minimized if these synthesis filters are chosen, which would achieve perfect reconstruction in lossless coding. The globally optimum filter bank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. A novel method for the determination of optimal bit allocation to subbands of the filter banks with optimized quantizers is also developed. The results are evaluated experimentally by comparison of the optimum uniformly split subband image coding scheme to classical logarithmically-split filter bank (wavelet) coding methods.     

Structure of spatio-temporal prefilters for conditional-replenishment video coders

A desirable integrated structure for conditional-replenishment video prefilters has been found experimentally to be unstable if too much spatial filtering is used. Analysis indicates a number of possible solutions; one which has been implemented is the separation of spatial and temporal sections.     

Direct-feedback coders: Design and performance with television signals

Direct-feedback coding is a refinement on the well-known differential coding method. Two filters are used at the transmitter of a direct-feedback coder; one connected in series with the input and the other in the forward path of a feedback loop that contains the quantizer. The first filter preemphasizes the signal and determines the overload characteristic of the coder; the other filter shapes the quantization noise and sets the stability of the feedback. At the receiver a filter reconstitutes the signal spectrum and deemphasizes the noise. For television the preemphasis should he a short time-constant differentiator, the deemphasis a short time integrator, and the feedback filter a long time integrator. Conventional differential coders use a single filter in the feedback path both to provide preemphasis and to shape the feedback characteristic, so the design is a compromise. Compared with direct-feedback coding they usually have less feedback gain and a larger time constant in the preemphasis and deemphasis, consequently, the contouring noise is more visible and the streaking caused by transmission error is longer. Although only application to television is considered, the methods have wider use. General formulae are given for the output noise and optimum filter characteristics; they take into account signal spectra, frequency weighting for noise, sampling rate, quantization step size, and an overload parameter. Measurements on real coders, operating on TV signals, and digital simulations confirm the results.     

The design of joint source and channel trellis waveform coders

The generalized Lloyd algorithm is applied to the design of joint source and channel trellis waveform coders to encode discrete-time continuous-amplitude stationary and ergodic sources operating over discrete memoryless noisy channels. Experimental results are provided for independent and autoregressive Gaussian sources, binary symmetric channels, and absolute error and squared error distortion measures. Performance of the joint codes is compared with the tandem combination of a trellis source code and a trellis channel code on the independent Gaussian source using the squared error distortion measure operating over an additive white Gaussian noise channel. It is observed that the jointly optimized codes achieve performance close to or better than that of separately optimized tandem codes of the same constraint length. Performance improvement via a predictive joint source and channel trellis code is demonstrated for the autoregressive Gaussian source using the squared error distortion measure.