Anubha Gupta

A new approach for estimation of statistically matched wavelet

This paper presents a new approach for the estimation of wavelets that is matched to a given signal in the statistical sense. Based on this approach, a number of new methods to estimate statistically matched wavelets are proposed. The paper first proposes a new method for the estimation of statistically matched two-band compactly supported biorthogonal wavelet system. Second, a new method is proposed to estimate statistically matched semi-orthogonal two-band wavelet system that results in compactly supported or infinitely supported wavelet. Next, the proposed method of estimating two-band wavelet system is generalized to M-band wavelet system. Here, the key idea lies in the estimation of analysis wavelet filters from a given signal. This is similar to a sharpening filter used in image enhancement. The output of analysis highpass filter branch is viewed to be equivalent to an error in estimating the middle sample from the neighborhood. To minimize this error, a minimum mean square error (MMSE) criterion is employed. Since wavelet expansion acts like Karhunen-Loe/spl grave/ve-type expansion for generalized 1/f/sup /spl beta// processes, it is assumed that the given signal is a sample function of an mth-order fractional Brownian motion. Therefore, the autocorrelation structure of a generalized 1/f/sup /spl beta// process is used in the estimation of analysis filters using the MMSE criterion. We then present methods to design a finite impulse response/infinite impulse response (FIR/IIR) biorthogonal perfect reconstruction filterbank, leading to the estimation of a compactly supported/infinitely supported statistically matched wavelet. The proposed methods are very simple. Simulation results to validate the proposed theory are presented for different synthetic self-similar signals as well as music and speech clips. Estimated wavelets for different signals are compared with standard biorthogonal 9/7 and 5/3 wavelets for the application of compression and are shown to have better results.

A new method of estimating wavelet with desired features from a given signal

This paper proposes a new method of estimating both biorthogonal compactly supported as well as semi-orthogonal infinitely/compactly supported wavelet from a given signal. The method is based on maximizing projection of the given signal onto successive scaling subspace. This results in minimization of energy of signal in the wavelet subspace. The idea used to estimate analysis wavelet filter is similar to a sharpening filter used in image enhancement. First, a new method is proposed that helps in the design of 2-band FIR biorthogonal perfect reconstruction filter bank from a given signal. This leads to the design of biorthogonal compactly supported wavelet. It is also shown that a wavelet with desired support as well as desired number of vanishing moments can be designed with the proposed method. Next, a method is proposed to design semi-orthogonal wavelets that are usually infinitely supported wavelets. Here, corresponding to FIR analysis filters, the resulting synthesis filters are IIR filters that satisfy the property of perfect reconstruction.

Variable Step-Size LMS Algorithm for Fractal Signals

This paper presents a novel variable step-size LMS (VSLMS) algorithm for tracking signals from the Gaussian 1/fbeta family of fractal signals that are inherently nonstationary. The proposed algorithm differs from the existing VSLMS algorithms in the following ways: 1) it deals with a specific class of nonstationary signals, 2) it utilizes a nondiagonal step-size matrix which is simultaneously diagonalizable with the auto-covariance matrix of the input signal, 3) in the decoupled weight vector space, one of the step-size parameters requires time-varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step-size parameters are time-invariant, and 4) it computes the step-size matrix by estimating the Hurst exponent required to characterize the statistical properties of the signal at the input of the adaptive filter. The experimental setup of an adaptive channel equalizer is considered for equalization of fractal signals transmitted over stationary AWGN channel. The performance of the proposed fractal-based variable step-size least mean square (FB-VSLMS) algorithm is compared with the unsigned VSLMS algorithm and is observed to be better for the class of nonstationary signals considered.

Some Studies on the Structure of Covariance Matrix of Discrete-Time fBm

This paper presents some results on the structure of autocovariance matrix of discrete-time fractional Brownian motion. Since these processes are nonstationary, the autocovariance matrix is a function of time. The eigenvalues associated with the autocovariance matrix are dependent on Hurst exponent characterizing the discrete-time fractional Brownian motion. However, it is seen that only one eigenvalue of this autocovariance matrix depends on time index n in the asymptotic sense, and it increases as the time index increases. All other eigenvalues are observed to be invariant with time index in the asymptotic sense. It is observed that the eigenvectors associated with these eigenvalues have an interesting structure and these eigenvectors can be used as filters of an M-band orthogonal wavelet system. The eigenvector associated with the time-varying eigenvalue is a lowpass filter. The subband signal from this lowpass filtered branch imbibes the nonstationary attribute of the input process and is a nonstationary signal whereas all other subband signals are stationary in nature.

Characterization of Discrete-time Fractional Brownian motion

In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time index n and it increases as the time index of the auto-covariance matrix increases. All other eigenvalues are observed to be invariant with time index n in an asymptotic sense. The eigenvectors associated with these eigenvalues also have a fixed structure and represent different frequency channels. The eigenvector associated with the time-varying eigenvalue is a low pass filter

Sparsity based UWB receiver design in additive impulse noise channels

Ultra wide-band (UWB) technology is suitable for high data rate short range wireless communication, localization, and imaging techniques. In many applications, UWB devices may be operating in environments with impulse noise sources or narrow band interferers, called as impulse interferer. Impulse noise of high amplitude and random occurrences can overlap a UWB signal making UWB signal recovery difficult at the receiver end. The conventional UWB receiver is not optimal for impulse noise since they are designed for additive Gaussian noise assumption. In this paper, we propose a robust UWB receiver designed to mitigate the detrimental effects of impulse noise by exploiting the distinct characteristics of the signal and impulse noise. The bit error rate (BER) performance of binary phase shift modulated UWB pulses is demonstrated in the presence of impulse noise using the proposed receiver design. Simulation results establish robustness of the proposed method to the presence of additive impulse noise.

A New Sparse Signal-Matched Measurement Matrix for Compressive Sensing in UWB Communication

Ultra wideband (UWB) technology is suitable for high data rate short range wireless communication, localization, and imaging techniques. However, UWB systems require high sampling rate and precise synchronization. In order to reduce the sampling rate, have precise synchronization, and for low power requirement, UWB systems are implemented using compressive or sub-Nyquist rate measured samples by exploiting the sparsity of the UWB signal. Compressive sensing (CS)-based UWB systems are being designed in two ways: 1) signal demodulation or detection is performed in the CS domain without full signal recovery at the front-end. Thus, demodulation or detection works on compressive measurements. However, system performance deteriorates in the CS domain as compared with full Nyquist rate sampling and 2) after, Nyquist rate signal is recovered using efficient algorithms at the front-end, the signal demodulation or detection is performed using the conventional receiver. Thus, one requires an efficient CS/sampling of signal measurement at the front-end for better system performance for both the cases stated earlier. In this paper, we propose a deterministic (partial) UWB waveform-matched measurement matrix. The proposed measurement matrix has a circulant structure and is sparse in nature. The proposed matrix is easy to implement in hardware and is operationally time efficient as needed in a practical system. The bit error rate performance of the corresponding UWB system and the operational time complexity with the proposed measurement matrix are better as compared with the existing measurement matrices in the CS domain for both the above receiver designs. The efficacy of the proposed measurement matrix is verified through extensive simulations in both the additive white Gaussian noise and multipath communication environments. In addition, we have also compared other desirable properties of the proposed measurement matrix with the existing measurement matrices.

Signal-matched wavelet design via lifting using optimization techniques

This paper proposes design of signal-matched wavelets via lifting. The design is modular owing to lifting framework wherein both predict and update stage polynomials are obtained from the given signal. Successive predict stages are designed using the least squares criterion, while the update stages are designed with total variation minimization on the wavelet approximation coefficients. Different design strategies for compression and denoising are presented. The efficacy of matched-wavelets is illustrated on transform coding gain and signal denoising.

DCT Domain Message Embedding in Spread-Spectrum Steganography System

Spread-spectrum steganographic (SSIS) method offers high payload and robustness to additive noise in transmission channel but the visual quality of image is distorted and exact data recovery may not be satisfied. DCT-domain message hiding based steganographic techniques provide high image imperceptibility and exact data recovery in absence of noise. In this paper, we combined the best of SSIS and DCT-domain hiding to provide high image imperceptibility and robustness to noise. We demonstrate our proposed algorithm through experiments on additive noise and jpeg compression attacks in the transmitted channel.

A Non-coherent UWB receiver using signal cluster sparsity

The ultra-wide band (UWB) technology can be used for low cost and low power applications such as body area networks, IoT based applications, wireless sensor networks and high data rate short range wireless communications. In the UWB literature, non-coherent energy detector (ED) receiver is proposed to reduce receiver implementation complexity by avoiding the complex channel estimation process and relaxing the precise synchronization requirement. However, the ED receiver performance is sensitive to the integration interval, and too large or small value of integration interval degrades the UWB receiver performance. In this paper, we propose a non-coherent UWB receiver by exploiting the cluster-sparsity of the received UWB signal. The proposed receiver structure enhances the signal-to-noise ratio at the receiver output as compared to the ED by barring inter-clusters noise accumulation. The bit error rate (BER) performance of the proposed non-coherent receiver for time-hopping binary pulse position modulation UWB system is analyzed using IEEE 802.15.4a channel. The proposed receiver design does not require any training and optimization process, and provides 1–3 dB BER performance gain as compared to the conventional ED receiver.