Nasir Ahmed

Detection of multiple sinusoids using an adaptive cascaded structure

The purpose of this paper is to present a simple adaptive algorithm for detecting and tracking a sinusoid in broadband noise, while at the same time improving its signal-to-noise ratio (SNR).

Video Compression Using Conditional Replenishment and Motion Prediction

A study of a low-rate monochrome video compression system is presented in this paper. This system is a conditional-replenishment coder that uses two-dimensional Walsh-transform coding within each video frame. The conditional-replenishment algorithm works by transmitting only the portions of an image that are changing in time. This system is augmented with a motion-prediction algorithm that measures spatial displacement parameters from frame to frame, and codes the data using these parameters. A comparison is made between the conditional-replen-ishment system with, and without, the motion-prediction algorithm. Subsampling in time is used to maintain the data rate at a fixed value. Average bit rates of 1 bit/picture element (pel) to 1/16 bit/pel are considered. The resultant performance of the compression simulations is presented in terms of the average frame rates produced.

Instantaneous Frequency Estimation Using Adaptive Linear Predictor Weights

A computationally efficient scheme for estimating the digital instantaneous frequencies of narrowband inputs is introduced. The frequency estimates are obtained by searching for minima of the inverse input power spectrum. This spectrum is estimated at each input sample from the weights of an adaptive linear predictor which uses the LMS (least mean square) algorithm to update its weights. The related minima are sought via an iterative search algorithm, referred to as the iterative frequency estimator. This algorithm is computationally more efficient than available methods, and also provides a higher resolution. Simulation results are included; these include tracking of random message sequences in FM signals, and the formant frequency estimation of speech.

DCT-based scheme for lossless image compression

In this paper, a new method to achieve lossless compression of 2D images based on the discrete cosine transform (DCT) is proposed. This method quantizes the high energy DCT coefficients in each block, finds an inverse DCT from only these quantized coefficients, and forms an error residual sequence to be coded. Furthermore, a simple delta modulation scheme is performed on the coefficients that exploits correlation between high energy DCT coefficients in neighboring blocks of an image. The resulting sequence is compressed by using an entropy coder, and simulations show the results to be promising and more effective than just simply performing entropy coding on original raw image data.

How I came up with the discrete cosine transform

During the late sixties and early seventies, there was a great deal of research activity related to digital orthogonal transforms and their use for image data compression. As such, there were a large number of transforms being introduced with claims of better performance relative to others transforms. Such comparisons were typically made on a qualitative basis, by viewing a set of “standard” images that had been subjected to data compression using transform coding techniques. At the same time, a number of researchers were doing some excellent work on making comparisons on a quantitative basis. In particular, researchers at the University of Southern California’s Image Processing Institute (Bill Pratt, Harry Andrews, Ali Habibi, and others) and the University of California at Los Angeles (Judea Pearl) played a key role. In this regard, the variance criterion and the rate distortion criterion were developed and used extensively as performance measures for evaluating image data compression. In addition, the Karhunen-Loeve transform (KLT) evolved as the optimal transform for comparison purposes. With this as background, I can now address the DCT issue. What intrigued me was that the KLT was indeed the optimal transform on the basis of the meansquare-error criterion and the first-order Markov process model, and yet there was no efficient algorithm available to compute it. As such, the focus of my research was to determine whether it would be possible to come up with a good approximation to the KLT that could be computed efficiently. An approach that I thought might be worth looking into was Chebyshev interpolation, a neat discussion of which was available in a text book (Computer Evaluation of Mathematical Functions, by C. T. Fike, Prentice-Hall, 1968, Sections 7.4 and 7.5). This was in early 1972, and I wrote a proposal to the National Science Foundation (NSF)

Optical diffraction tomography for latent image metrology

Optical diffraction tomography (ODT) attempts to reconstruct the complex refractive index profile of an object by inverting its backscattered and/or transmitted fields. Owing to its integral formulation of the diffracted plane, the inverse scattering problem in ODT, i.e., reconstructing the object from its diffracted field, can be linearized via the Born approximation. The validity range of the Born approximation is limited to weakly scattering objects, or objects whose refractive index distributions are slowly varying and comparable in magnitude to their background. Such constraints are easily met in microlithography when considering the area of latent image metrology. Indeed, latent images are generally characterized by their relatively small and slowly varying refractive indices. An algorithm is presented for reconstructing the refractive index distribution of latent images from their first (+1) and second (+2) reflected diffraction orders at the Bragg angle.

Chapter 12 – Adaptive Filtering

Publisher Summary The term adaptive filtering implies that filter parameters such as bandwidth and notch frequency change with time. As such, the coefficients of adaptive filters vary with time. This chapter discusses a subset of FIR adaptive filters of which weights are changed by a technique called steepest descent. This subset of adaptive filters is widely used and is described in terms of tapped-delay-line and lattice models. The chapter presents an introduction and working knowledge of such adaptive digital filters. It discusses some matrix operations that are used to derive a class of optimal least squares filters. The optimal solutions derived in the chapter involve autocorrelation matrices and cross-correlation vectors that are assumed to be known. In many applications, this is not the case. They may be difficult to estimate or the data statistics may be changing with time, that is, the data sequences may be nonstationary. In such cases, adaptive filtering techniques are employed. A useful algorithm in this regard is the least-mean-squares (LMS) algorithm. The notion of steepest descent plays a key role in arriving at the LMS algorithm. The chapter explores the implementation of LMS and modified LMS (MLMS) algorithms with the tapped-delay-line and lattice models and describes two models: (1) the one-step predictor model and (2) the filter model.

On Laguerre expansions and systolic arrays

Discrete-time Laguerre sequences are effective for representing sequences in the form of orthogonal expansions. The main objective of this communication is to propose a systolic-array implementation for finite-duration Laguerre expansions.

On an adaptive noise cancellation application for radar

The purpose of this correspondence is to introduce a novel application of adaptive noise cancellation related to a class of radar signals.

Vectorcardiographic Data Compression via Walsh And Cosine Transforms

In this study the use of two-dimensional transforms for compressing human vectorcardiographic (VCG) data is investigated. The VCG signal is two-dimensional in nature, one dimension consisting of the spatial axes and the other consisting of the samples in time along a particular spatial axis. The discrete cosine transform (DCT) and the Walsh-Hadamard transform (WHT) were used. The variance criterion was employed for selecting components to be retained. The training set was formed from 225 VCG records from three different diagnostic classes. The DCT yielded compression ratios from 3:1 to 5:1, while compression ratios of around 2:1 were obtained with the WHT.