Rajeev Nongpiur

Impulse noise removal in speech using wavelets

A new method for removing impulse noise from speech in the wavelet transform domain is proposed. The method utilizes the multi-resolution property of the wavelet transform, which provides finer time resolution at the higher frequencies than the short-time Fourier transform (STFT), to effectively identify and remove impulse noise. It uses two features of speech to discriminate speech from impulse noise: one is the slow time-varying nature of speech and the other is the Lipschitz regularity of the speech components. On the basis of these features, an algorithm has been developed to identify and suppress wavelet coefficients that correspond to impulse noise. Experiment results show that the new method is able to significantly reduce impulse noise without degrading the quality of the speech signal or introducing any audible artifacts.

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

A new optimization method for the design of nearly linear-phase IIR digital filters that satisfy prescribed specifications is proposed. The group-delay deviation is minimized under the constraint that the passband ripple and stopband attenuation are within the prescribed specifications and either a prescribed or an optimized group delay can be achieved. By representing the filter in terms of a cascade of second-order sections, a non-restrictive stability constraint characterized by a set of linear inequality constraints can be incorporated in the optimization algorithm. An additional feature of the method, which is very useful in certain applications, is that it provides the capability of constraining the maximum gain in transition bands to be below a prescribed level. Experimental results show that filters designed using the proposed method have much lower group-delay deviation for the same passband ripple and stopband attenuation when compared with corresponding filters designed with several state-of-the-art competing methods.

Design of IIR Digital Differentiators Using Constrained Optimization

A new optimization method for the design of fullband and lowpass IIR digital differentiators is proposed. In the new method, the passband phase-response error is minimized under the constraint that the maximum passband amplitude-response relative error is below a prescribed level. For lowpass IIR differentiators, an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high-frequency noise that may be present. Extensive experimental results are included, which show that the differentiators designed using the proposed method have much smaller maximum phase-response error for the same passband amplitude-response error and stopband constraints when compared with several differentiators designed using state-of-the-art competing methods.

L -infinity norm design of linear-phase robust broadband beamformers using constrained optimization

A new method for the design of linear-phase robust far-field broadband beamformers using constrained optimization is proposed. In the method, the maximum passband ripple and minimum stopband attenuation are ensured to be within prescribed levels, while at the same time maintaining a good linear-phase characteristic at a prescribed group delay in the passband. Since the beamformer is intended primarily for small-sized microphone arrays where the microphone spacing is small relative to the wavelength at low frequencies, the beamformer can become highly sensitive to spatial white noise and array imperfections if a direct minimization of the error is performed. Therefore, to limit the sensitivity of the beamformer the optimization is carried out by constraining a sensitivity parameter, namely, the white noise gain (WNG) to be above prescribed levels across the frequency band. Two novel design variants have been developed. The first variant is formulated as a convex optimization problem where the maximum error in the passband is minimized, while the second variant is formulated as an iterative optimization problem and has the advantage of significantly improving the linear-phase characteristics of the beamformer under any prescribed group delay or linear-array configuration. In the second variant, the passband group-delay deviation is minimized while ensuring that the maximum passband ripple and stopband attenuation are within prescribed levels. To reduce the computational effort in carrying out the optimization, a nonuniform variable sampling approach over the frequency and angular dimensions is used to compute the required parameters. Experiment results show that beamformers designed using the proposed methods have much smaller passband group-delay deviation for similar passband ripple and stopband attenuation than a modified version of an existing method.

Maximizing the Signal-to-Alias Ratio in Non-Uniform Filter Banks for Acoustic Echo Cancellation

A new method for designing non-uniform filter-banks for acoustic echo cancellation is proposed. In the method, the analysis prototype filter design is framed as a convex optimization problem that maximizes the signal-to-alias ratio (SAR) in the analysis banks. Since each sub-band has a different bandwidth, the contribution to the overall SAR from each analysis bank is taken into account during optimization. To increase the degrees of freedom during optimization, no constraints are imposed on the phase or group delay of the filters; at the same time, low delay is achieved by ensuring that the resulting filters are minimum phase. Experimental results show that the filter bank designed using the proposed method results in a sub-band adaptive filter with a much better echo return loss enhancement (ERLE) when compared with existing design methods.

Synthesis of Linear and Planar Arrays With Minimum Element Selection

A new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed. In the method, the number of elements in an array is minimized while constraining the amplitude-response error in the mainlobe region, the attenuation in the sidelobe region, and the array dimensions. An iterative constrained optimization method is used where the amplitude-response error is linearly approximated at each iteration while concurrently minimizing a re-weighted L1 norm of the array coefficients. To ensure robustness of the array, we constrain a sensitivity parameter, namely, the white noise gain, to be above a prescribed level. Furthermore, the method also provides the additional flexibility of controlling the array dimensions, symmetry properties, and element positions of the array. Two variants have been developed: In the first variant, both the array coefficients and the positions of the elements are optimized; in the second variant, only the array coefficients are optimized while the elements are fixed at predefined positions. Experimental comparisons with several state-of-the-art competing methods show that the proposed method provides greater flexibility of controlling the robustness, beampattern response error, array dimensions, and element positions while at the same time the number of elements is less than or equal to that of the competing methods.

Impulse-noise suppression in speech using the stationary wavelet transform

An approach for detecting and removing impulse noise from speech using the wavelet transform is proposed. The approach utilizes the multi-resolution property of the wavelet transform, which provides finer time resolution at higher frequencies than the short-time Fourier transform to effectively identify and remove impulse noise. The paper then describes how the impulse-detection performance is dependent on certain wavelet features and their relationships with the impulse noise and the underlying speech signal. Performance comparisons carried out with an existing method show that the wavelet approach yields much better features for detecting the impulses. To remove the impulses, an algorithm that uses the stationary wavelet transform has been developed. The algorithm uses a two-step approach where the wavelet coefficients corresponding to the impulses are suppressed in the first step and then substituted by suitable coefficients located within the vicinity of the impulse in the second step. Performance evaluations with an existing method show that the proposed algorithm gives superior results.

Design of minimax broadband beamformers that are robust to microphone gain, phase and position errors

Broadband beamformers with small-size microphone arrays are known to be highly sensitive to microphone imperfections. A new method for the design of minimax broadband beamformers that are robust to microphone gain, phase, and position errors is proposed. In the method, the maximum variations in the microphone errors are used in formulating a convex optimization problem where the worst-case passband error is minimized under the constraint that the worst-case stopband error is below a prescribed level. To include the microphone imperfections in the optimization problem, we developed a suitable model that incorporates the variations due to the microphone errors and at the same time is efficient to compute. An important advantage of the proposed method is the availability of corresponding worst-case passband- and stopband-error bounds for the beamformer that has been designed; a second advantage is that it does not require the probability distributions of microphone errors. We then describe a two-phase method where the proposed method is used in the first phase to derive the passband and stopband error constraints for solving an optimization problem in the second phase where the white noise gain (WNG) of the beamformer is maximized. In our experiments, we compare beamformers designed using the proposed method, the two-phase method and a modified version of a competing method. Experimental results show that beamformers designed using the proposed method have much better performance than those of the modified competing method and comparable performance with those of the two-phase method; however, unlike the two-phase method, the proposed method provides the additional guarantee that the errors will always lie within the worst-case error bounds.

Design of optimal wavelets for detecting impulse noise in speech

Removal of impulse noise from speech in the wavelet domain has been found to be very effective due to the multi-resolution property of the wavelet transform and the ease of removing the impulses in that domain. A critical factor that affects the performance of the impulse-removal system is the effectiveness of the impulse detection algorithm. To this end, we propose a new method for designing orthogonal wavelets that are optimized for detecting impulse noise in speech. In the method, the characteristics of the impulse noise and the underlying speech signal are taken into account and a convex optimization problem is formulated for deriving the optimal wavelet for a given support size. Performance comparison with other well-known wavelets show that the wavelets designed using the proposed method have much better impulse detection properties.

Design of minimax robust broadband beamformers with optimized microphone positions

A new method for the design of robust minimax far-field broadband beamformers with optimized microphone positions is proposed. The method is formulated as an iterative optimization problem where the maximum passband magnitude response error is minimized and the microphone positions are optimized while ensuring that the minimum stopband attenuation is above a prescribed level. To maintain robustness, we constrain a sensitivity parameter, namely, the white noise gain, to be above prescribed levels across the frequency band. An additional feature of the method, which is quite useful in certain applications, is that it provides the capability of constraining the gain in the transition band to always lie below the maximum gain in the passband. Performance comparisons with existing methods show that the optimization of the microphone positions results in beamformers with superior performance.