| 1. |
- Sadasivan, Jishnu, et al.
(författare)
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Signal denoising using the minimum-probability-of-error criterion
- 2020
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Ingår i: APSIPA TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING. - : CAMBRIDGE UNIV PRESS. - 2048-7703. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- We consider signal denoising via transform-domain shrinkage based on a novel risk criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an epsilon-neighborhood of the true value. The underlying parameter is assumed to be deterministic. The MPE, similar to the mean-squared error (MSE), depends on the ground-truth parameter, and therefore, has to be estimated from the noisy observations. The optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of error is integrated over epsilon, it leads to the expected l(1) distortion. The proposed MPE and l(1) distortion formulations are applicable to various noise distributions by invoking a Gaussian mixture model approximation. Within the realm of MPE, we also develop a specific extension to subband shrinkage. The denoising performance of MPE turns out to be better than that obtained using the minimum MSE-based approaches formulated within Stein's unbiased risk estimation (SURE) framework, especially in the low signal-to-noise ratio (SNR) regime. Performance comparisons with three benchmarking algorithms carried out on electrocardiogram signals and standard test signals taken from the Wavelab toolbox show that the MPE framework results in SNR gains particularly for low input SNR.
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| 2. |
- Venkitaraman, Arun, et al.
(författare)
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A Technique to Compute Smooth Amplitude, Phase, and Frequency Modulations From the Analytic Signal
- 2012
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Ingår i: IEEE Signal Processing Letters. - : IEEE Signal Processing Society. - 1070-9908 .- 1558-2361. ; 19:10, s. 623-626
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Tidskriftsartikel (refereegranskat)abstract
- Gabor’s analytic signal (AS) is a unique complexsignal corresponding to a real signal, but in general, it admitsinfinitely-many combinations of amplitude and frequency modu-lations (AM and FM, respectively). The standard approach is toenforce a non-negativity constraint on the AM, but this results indiscontinuities in the corresponding phase modulation (PM), andhence, an FM with discontinuities particularly when the under-lying AM-FM signal is over-modulated. In this letter, we analyzethe phase discontinuities and propose a technique to computesmooth AM and FM from the AS, by relaxing the non-negativityconstraint on the AM. The proposed technique iseffective athandling over-modulated signals. We present simulation results tosupport the theoretical calculations.
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| 3. |
- Venkitaraman, Arun, et al.
(författare)
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Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation
- 2014
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Ingår i: IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING. - 2329-9290. ; 22:6, s. 1023-1036
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Tidskriftsartikel (refereegranskat)abstract
- Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated-frequency-modulated (AM-FM) signals using a signal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor's AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.
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| 4. |
- Venkitaraman, Arun, et al.
(författare)
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Fractional Hilbert transform extensions and associated analytic signal construction
- 2014
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Ingår i: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 94, s. 359-372
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Tidskriftsartikel (refereegranskat)abstract
- The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations.
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| 5. |
- Venkitaraman, Arun, et al.
(författare)
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On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal
- 2013
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Ingår i: IEEE Signal Processing Letters. - : IEEE Signal Processing Society. - 1070-9908 .- 1558-2361. ; 20:12, s. 1187-1190
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Tidskriftsartikel (refereegranskat)abstract
- The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.
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| 6. |
- Venkitaraman, Arun, et al.
(författare)
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Temporal Envelope Fit of Transient Audio Signals
- 2013
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Ingår i: IEEE Signal Processing Letters. - : IEEE Signal Processing Society. - 1070-9908 .- 1558-2361. ; 20:12, s. 1191-1194
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Tidskriftsartikel (refereegranskat)abstract
- We address the problem of temporal envelope modeling for transient audio signals. We propose the Gamma distribution function (GDF) as a suitable candidate for modeling the envelope keeping in view some of its interesting properties such as asymmetry, causality, near-optimal time-bandwidth product, controllability of rise and decay, etc. The problem of finding the parameters of the GDF becomes a nonlinear regression problem. We overcome the hurdle by using a logarithmic envelope fit, which reduces the problem to one of linear regression. The logarithmic transformation also has the feature of dynamic range compression. Since temporal envelopes of audio signals are not uniformly distributed, in order to compute the amplitude, we investigate the importance of various loss functions for regression. Based on synthesized data experiments, wherein we have a ground truth, and real-world signals, we observe that the least-squares technique gives reasonably accurate amplitude estimates compared with other loss functions.
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| 7. |
- Venkitarman, Arun, et al.
(författare)
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Auditory-motivated Gammatone wavelet transform
- 2014
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 94, s. 608-619
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Tidskriftsartikel (refereegranskat)abstract
- The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals.
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