Log Magnitude Spectrum Research Articles

Gamma Boltzmann Machine for Audio Modeling

This paper presents an energy-based probabilistic model that handles nonnegative data in consideration of both linear and logarithmic scales. In audio applications, magnitude of time-frequency representation, including spectrogram, is regarded as one of the most important features. Such magnitude-based features have been extensively utilized in learning-based audio processing. Since a logarithmic scale is important in terms of auditory perception, the features are usually computed with a logarithmic function. That is, a logarithmic function is applied within the computation of features so that a learning machine does not have to explicitly model the logarithmic scale. We think in a different way and propose a restricted Boltzmann machine (RBM) that simultaneously models linear- and log-magnitude spectra. RBM is a stochastic neural network that can discover data representations without supervision. To manage both linear and logarithmic scales, we define an energy function based on both scales. This energy function results in a conditional distribution (of the observable data, given hidden units) that is written as the gamma distribution, and hence the proposed RBM is termed gamma-Bernoulli RBM. The proposed gamma-Bernoulli RBM was compared to the ordinary Gaussian-Bernoulli RBM by speech representation experiments. Both objective and subjective evaluations illustrated the advantage of the proposed model.

On the use of blind channel response estimation and a residual neural network to detect physical access attacks to speaker verification systems

Spoofing attacks have been acknowledged as a serious threat to automatic speaker verification (ASV) systems. In this paper, we are specifically concerned with replay attack scenarios. As a countermeasure to the problem, we propose a front-end based on the blind estimation of the channel response magnitude and as a back-end a residual neural network. Our hypothesis is that the magnitude response of the channel, obtained by subtracting the log-magnitude spectrum of the observed signal from the prediction of the log-magnitude spectrum average of the observed signal’s clean counterpart, will capture the nuances of room ambiences, recordings and playback devices. The performance of these features is investigated on a benchmark back-end, based on a Gaussian mixture model and on a deep neural network classifier. Our experiments are performed on the 2017 and 2019 Automatic Speaker Verification Spoofing and Countermeasures Challenge (ASVspoof) datasets. The benchmark systems are the same as used in the challenges and are based on constant-Q cepstral coefficients (CQCC) and linear-frequency cepstral coefficients (LFCC) features. Experimental results on the 2017 dataset show that the proposed method outperforms the two benchmarks, providing equal-error rates (EER) as low as 7.57% and 11.64%, respectively, for the development and evaluation sets. On the ASVspoof 2019 dataset, in turn, the proposed method outperformed the benchmark using a residual neural network as back-end by yielding tandem detection cost function (t-DCF) and EER as low as 0.1086 and 4.26% on the evaluation set. Lastly, an instrumental (objective) quality assessment is performed on the two datasets and the impact of quality variability on spoofing detection accuracy is discussed.

Discriminative features based on modified log magnitude spectrum for playback speech detection

In order to improve the performance of hand-crafted features to detect playback speech, two discriminative features, constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients, are proposed for playback speech detection in this work. They rely on our findings that variance-based modified log magnitude spectrum and mean-based modified log magnitude spectrum can enhance the discriminative power between genuine speech and playback speech. Then constant-Q variance-based octave coefficients (constant-Q mean-based octave coefficients) can be obtained by combining variance-based modified log magnitude spectrum (mean-based modified log magnitude spectrum), octave segmentation, and discrete cosine transform. Finally, constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients are evaluated on ASVspoof 2017 corpus version 2.0 and ASVspoof 2019 physical access, respectively. Experimental results show that variance-based modified log magnitude spectrum and mean-based modified log magnitude spectrum can produce discriminative features toward playback speech. Further results on the two databases show that constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients can perform better than some common features, such as mel frequency cepstral coefficients and constant-Q cepstral coefficients.

Modulation-Domain Kalman Filtering for Monaural Blind Speech Denoising and Dereverberation

We describe a monaural speech enhancement algorithm based on modulation-domain Kalman filtering to blindly track the time–frequency log-magnitude spectra of speech and reverberation. We propose an adaptive algorithm that performs blind joint denoising and dereverberation, while accounting for the inter-frame speech dynamics, by estimating the posterior distribution of the speech log-magnitude spectrum given the log-magnitude spectrum of the noisy reverberant speech. The Kalman filter update step models the non-linear relations between the speech, noise, and reverberation log spectra. The Kalman filtering algorithm uses a signal model that takes into account the reverberation parameters of the reverberation time $T_{60}$ and the direct-to-reverberant energy ratio (DRR) and also estimates and tracks $T_{60}$ and the DRR in every frequency bin to improve the estimation of the speech log spectrum. The proposed algorithm is evaluated in terms of speech quality, speech intelligibility, and dereverberation performance for a range of reverberation parameters and reverberant speech to noise ratios, in different noises, and is also compared to competing denoising and dereverberation techniques. Experimental results using noisy reverberant speech demonstrate the effectiveness of the enhancement algorithm.

Cepstral distance based channel selection for distant speech recognition

Shifting from a single to a multi-microphone setting, distant speech recognition can be benefited from the multiple instances of the same utterance in many ways. An effective approach, especially when microphones are not organized in an array fashion, is given by channel selection (CS), which assumes that for each utterance there is at least one channel that can improve the recognition results when compared to the decoding of the remaining channels. In order to identify this most favourable channel, a possible approach is to estimate the degree of distortion that characterizes each microphone signal. In a reverberant environment, this distortion can vary significantly across microphones, for instance due to the orientation of the speaker’s head. In this work, we investigate on the application of cepstral distance as a distortion measure that turns out to be closely related to properties of the room acoustics, such as reverberation time and direct-to-reverberant ratio. From this measure, a blind CS method is derived, which relies on a reference computed by averaging log magnitude spectra of all the microphone signals. Another aim of our study is to propose a novel methodology to analyze CS under a wide set of experimental conditions and setup variations, which depend on the sound source position, its orientation, and the microphone network configuration. Based on the use of prior information, we introduce an informed technique to predict CS performance. Experimental results show both the effectiveness of the proposed blind CS method and the value of the aforementioned analysis methodology. The experiments were conducted using different sets of real and simulated data, the latter ones derived from synthetic and from measured impulse responses. It is demonstrated that the proposed blind CS method is well related to the oracle selection of the best recognized channel. Moreover, our method outperforms a state-of-the-art one, especially on real data.

Hamming Generalized Low Time Liftered Cepstral Analysis

The main aim of this experiment is to separate the excitation of vocal tract components of the given speech signal by cepstral analysis. The first step is to convert the speech into short-term segments of size 15-20 ms. Then multiplication of each frame is carried out with the help of Hamming Window. The representation of short term speech in cepstral analysis is computed by finding the IDFT of log magnitude spectrum. In order to extract the deconvolved vocal tract and excitation component from the cepstrum liftering has to be done.

On the harmonic-to-noise ratio as an acoustic cue of vocal timbre of Parkinson speakers

Abstract The relevance of the harmonic-to-noise ratio (HNR) and glottal cycle length jitter as cues of the vocal timbre of Parkinson speakers is investigated. HNR and vocal cycle length jitter are known to be suitable cues for the evaluation of the vocal timbre of dysphonic speakers. However, the question whether they are relevant descriptors of the voice quality of Parkinson speakers is still unanswered. Empirical mode decomposition (EMD) has been used to estimate the HNR by decomposing the log-magnitude spectrum of the speech signal into its harmonic, contour and noise components. Cycle length jitter has been estimated via the break-up by empirical mode decomposition of the cycle length time series into the intonation contour as well as the perturbations owing to tremor and jitter. HNR and cycle length jitter values of vowels [a] sustained by 205 Parkinson and 74 control speakers are in the same interval respectively and the differences are not statistically significant. Also, the standard deviations of the per-frame HNR values of an utterance do not differ statistically significantly between control and Parkinson speakers.

Speech dereverberation for enhancement and recognition using dynamic features constrained deep neural networks and feature adaptation

This paper investigates deep neural networks (DNN) based on nonlinear feature mapping and statistical linear feature adaptation approaches for reducing reverberation in speech signals. In the nonlinear feature mapping approach, DNN is trained from parallel clean/distorted speech corpus to map reverberant and noisy speech coefficients (such as log magnitude spectrum) to the underlying clean speech coefficients. The constraint imposed by dynamic features (i.e., the time derivatives of the speech coefficients) are used to enhance the smoothness of predicted coefficient trajectories in two ways. One is to obtain the enhanced speech coefficients with a least square estimation from the coefficients and dynamic features predicted by DNN. The other is to incorporate the constraint of dynamic features directly into the DNN training process using a sequential cost function. In the linear feature adaptation approach, a sparse linear transform, called cross transform, is used to transform multiple frames of speech coefficients to a new feature space. The transform is estimated to maximize the likelihood of the transformed coefficients given a model of clean speech coefficients. Unlike the DNN approach, no parallel corpus is used and no assumption on distortion types is made. The two approaches are evaluated on the REVERB Challenge 2014 tasks. Both speech enhancement and automatic speech recognition (ASR) results show that the DNN-based mappings significantly reduce the reverberation in speech and improve both speech quality and ASR performance. For the speech enhancement task, the proposed dynamic feature constraint help to improve cepstral distance, frequency-weighted segmental signal-to-noise ratio (SNR), and log likelihood ratio metrics while moderately degrades the speech-to-reverberation modulation energy ratio. In addition, the cross transform feature adaptation improves the ASR performance significantly for clean-condition trained acoustic models.

LPC-based formant enhancement method in Kalman filtering for speech enhancement

In this work, we are concerned by a new iterative Kalman filtering scheme where a linear predictor model parameters are estimated from noisy speech. However, when only noise-corrupted speech is available, the enhancement performance of the Kalman filter is somewhat dependent on the accuracy of the linear prediction coefficients (LPCs) and excitation variance estimates. Nevertheless, linear prediction based speech (LPC) analysis is known to be sensitive to the presence of additive noise. To overcome this problem we present in this paper an analysis and application of the LPC-based formant enhancement method by modifying the log magnitude spectrum of the LPC model and then re-evaluating new LPCs to be applied on the Kalman filter. These enhanced LPCs are useful indicator of Kalman filter performance. Our enhancement experiments use a NOIZEUS speech corpus where the proposed method achieves higher objective and subjective results compared with other enhancement methods.

Multiband vocal dysperiodicities analysis using empirical mode decomposition in the log-spectral domain

In this paper, empirical mode decomposition (EMD) is proposed as an alternative to decompose the log magnitude spectrum of the speech signal into its harmonic, envelope and noise components. The acoustic measure named harmonic-to-noise ratio (HNR) is used to summarize the degree of disturbance in the speech signal and consequently to evaluate the overall quality of the disordered voices produced by dysphonic speakers.Most approaches for HNR estimation have in common to involve the isolation of individual speech cycles or pseudo-harmonics/rhamonics in speech spectrum/cepstrum; however, this isolation cannot be carried out reliably in speech produced by severely hoarse speakers and may result in inaccurate HNR estimation. The EMD-based approach used in this study incorporates an appropriate procedure that estimates automatically the thresholds used by the clustering algorithm without knowledge of the fundamental frequency. The frequency range of the harmonic and noise components is divided into ten equally spaced intervals and the harmonic-to-noise ratios (HNRs) within each interval are used as independent variables to summarize the amount of perceived hoarseness.The proposed method is evaluated on a corpus comprising 251 normophonic and dysphonic speakers. Multiple correlation analysis carried out on HNRs from the different frequency bands shows that multi-band analysis based on empirical mode decomposition results in statistically significantly higher correlation of predicted scores with scores of perceived hoarseness over full-band analysis.Principal component analysis is carried out on the HNR measures obtained in the ten frequency bands. More than 97% of the total variance is explained by the first two principal components, PC1 and PC2. Experimental results show that the first principal component is interpretable in terms of the degree of the severity of hoarseness whereas the second principal component indicates whether the voice is high-pitched or low-pitched. It is shown that the first two principal components result in a high predictability of hoarseness scores.

SSVEP‐based BCI classification using power cepstrum analysis

The power cepstrum-based parameters for steady-state visually evoked potential (SSVEP) is proposed. To precisely represent the characteristics of frequency responses of a visually stimulated electroencephalography (EEG) signal, power cepstrum analysis is adopted to estimate the parameters in low-dimensional space. To represent the frequency responses of SSVEP, the log-magnitude spectrum of an EEG signal is estimated by fast Fourier transform. Subsequently, the discrete cosine transform is applied to linearly transform the log-magnitude spectrum into the cepstrum domain, and then generate a set of coefficients. Finally, a Bayesian decision model with a Gaussian mixture model is adopted to classify the responses of SSVEP. The experimental results demonstrated that the proposed approach was able to improve performance compared with previous approaches and was suitable for use in brain computer interface applications.

Speech enhancement using hidden Markov models in Mel-frequency domain

Hidden Markov model (HMM)-based minimum mean square error speech enhancement method in Mel-frequency domain is focused on and a parallel cepstral and spectral (PCS) modeling is proposed. Both Mel-frequency spectral (MFS) and Mel-frequency cepstral (MFC) features are studied and experimented for speech enhancement. To estimate clean speech waveform from a noisy signal, an inversion from the Mel-frequency domain to the spectral domain is required which introduces distortion artifacts in the spectrum estimation and the filtering. To reduce the corrupting effects of the inversion, the PCS modeling is proposed. This method performs concurrent modeling in both cepstral and magnitude spectral domains. In addition to the spectrum estimator, magnitude spectrum, log-magnitude spectrum and power spectrum estimators are also studied and evaluated in the HMM-based speech enhancement framework.The performances of the proposed methods are evaluated in the presence of five noise types with different SNR levels and the results are compared with several established speech enhancement methods especially auto-regressive HMM-based speech enhancement. The experimental results for both subjective and objective tests confirm the superiority of the proposed methods in the Mel-frequency domain over the reference methods, particularly for non-stationary noises.

Robustness of group delay representations for noisy speech signals

This paper demonstrates the robustness of group delay based features to additive noise. First, we analytically show the robustness of group delay based representations. The analysis makes use of the fact that, for minimum-phase signals, the group delay function can be represented in terms of the cepstral coefficients of the log-magnitude spectrum. Such a representation results in the speech spectrum dominating over the noise spectrum, both at low and high SNRs. Further, we experimentally demonstrate the robustness of the representation on a voice activity detection (VAD) task, comparing a group delay based VAD algorithm with standard VAD methods as well as a magnitude-spectrum based method.

Assessment of disordered voice via the first rahmonic

A number of studies have shown that the amplitude of the first rahmonic peak (R1) in the cepstrum can be usefully employed to indicate hoarse voice quality. The cepstrum is obtained by taking the inverse Fourier transform of the log-magnitude spectrum. In the present study, a number of spectral pre-processing steps are investigated prior to computing the cepstrum; the pre-processing steps include period-synchronous, period-asynchronous, harmonic-synchronous and harmonic-asynchronous spectral band-limitation analysis. The analysis is applied on both sustained vowels [a] and connected speech signals. The correlation between R1 (the amplitude of the first rahmonic) and perceptual ratings is examined for a corpus comprising 251 speakers. It is observed that the correlation between R1 and perceptual ratings increases when the spectrum is band-limited prior to computing the cepstrum. In addition, comparisons are made with a previously reported cepstral cue, cepstral peak prominence (CPP).

On the design of pole-zero approximations using a logarithmic error measure

For obtaining a pole-zero approximation of a linear, discrete-time system, a new method is presented which minimizes the squared difference between the log-magnitude spectrum of the system and that of the approximation. Using an iterative procedure, a locally optimal solution is found for the poles and zeros of the system approximation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frequency domain adaptive postfiltering for enhancement of noisy speech

This paper presents a new frequency-domain approach to implement an adaptive postfilter for enhancement of noisy speech. The postfilter is described by a set of DFT coefficients which suppress noise in the spectral valleys and allow for more noise in formant regions which is masked by the speech signal. First, we perform an LPC analysis of the noisy speech and calculate the log magnitude spectrum of the input speech. After identifying the formants and valleys (by a new method), the log magnitude spectrum is modified to obtain the postfilter coefficients. The filtering operation is also done in the frequency domain through an FFT and an overlap-add strategy to get the postfiltered speech. Experimental results on 8-kHz-sampled speech show that this new frequency-domain approach results in enhanced speech of better perceptual quality than obtained by a time-domain method. This new method is especially efficient in eliminating high frequency noise and in preserving the weaker, high frequency formants in sonorant sounds.

Speech of cochlear implant patients: a longitudinal study of vowel production.

Acoustic parameters were measured for vowels spoken in /hVd/ context by four postlingually deafened recipients of multichannel (Ineraid) cochlear implants. Three of the subjects became totally deaf in adulthood after varying periods of partial hearing loss; the fourth became totally deaf at age four. The subjects received different degrees of perceptual benefit from the prosthesis. Recordings were made before, and at intervals following speech processor activation. The measured parameters included F1, F2, F0, SPL, duration, and amplitude difference between the first two harmonic peaks in the log magnitude spectrum (H 1-H2). Numerous changes in parameter values were observed from pre- to post-implant, with differences among subjects. Many changes, but not all, were in the direction of normative data, and most changes were consistent with hypotheses about relations among the parameters. Some of the changes tended to enhance phonemic contrasts; others had the opposite effect. For three subjects, H 1-H2 changed in a direction consistent with measurements of their average air flow when reading; that relation was more complex for the fourth subject. The results are interpreted with respect to: characteristics of the individual subjects, including vowel identification scores; mechanical interactions among glottal and supraglottal articulations; and hypotheses about the role of auditory feedback in the control of speech production. Almost all the observed differences could be attributed to changes in the average settings of speaking rate, F0 and SPL, which presumably can be perceived without the need for spectral place information. Some observed F2 realignment may be attributable to the reception of spectral cues.

Speech processing using group delay functions

In this paper we demonstrate the feasibility of processing the Fourier transform (FT) phase of a speech signal to derive the smooth log magnitude spectrum corresponding to the vocal tract system. We exploit the additive property of the group delay function (negative derivative of the FT phase) to process the FT phase. We show that the rapid fluctuations in the log magnitude spectrum and the group delay function are caused by the zeroes of the z-transform of the excitation components of the speech signal. Zeroes close to the unit circle in the z-plane produce large amplitude spikes in the group delay function and mask the group delay information corresponding to the vocal tract system. We propose a technique to extract the vocal tract system component of the group delay function by using the spectral properties of the excitation signal.

Vowel acoustics in cochlear implant patients

Acoustic parameters were measured for vowels spoken in /hVd/ context by three postlingually deafened cochlear implant recipients. Two female subjects became deaf in adulthood; the male subject, in childhood. Recordings were made before and at intervals following processor activation. The measured parameters included formant frequencies, F0, SPL, duration, and amplitude difference between the first two harmonic peaks in the log magnitude spectrum (H1–H2). A number of changes were observed from pre‐ to post‐implant, with intersubject differences. The male subject showed changes in F1, vowel durations, and F0. These changes were consistent with one another; however, they were not necessarily in the direction of normalcy. On the other hand, the female subjects showed changes in F2, vowel durations, F0, and SPL, which were in the direction of normal values and, for some parameters, tended to enhance phonemic contrasts. For all three subjects, H1–H2 changed in a direction that was consistent with previously mad...

Pole-zero spectral modeling of EEG

This paper deals with the pole-zero spectral modeling of EEG by the methods based on the combination of homomorphic filtering and linear prediction. The homomorphic prediction method, which models the minimum phase equivalent of the signal, and the pole-zero decomposition method which models pole and zero spectra separately, are considered. These two methods yield similar performance for EEG. However, the latter has an edge over the former in providing a better spectral fit to the log magnitude spectrum, specifically with respect to valley region and the bandwidth of the spectral peak. The direct pole-zero modeling of EEG (without homomorphic filtering) has been found to affect the zero spectrum severely, resulting in an inaccurate spectral estimate. The zero estimates by the direct method, at least in some EEGs, indicate that in general, EEG is not a minimum phase signal. Even in cases where there is no indication of mixed phase nature of EEG, the spectral estimates obtained by the proposed methods are found to be far superior to the direct method. Furthermore, on comparison for the same number of parameters, these two methods are found to perform better than the Burg's all-pole modeling. The study is based on real EEGs recorded from three different subjects.