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This chapter is devoted to the discussion of a hybrid frequency-time CAD tool especially designed for the efficient numerical simulation of nonlinear electronic radio frequency circuits operating in an aperiodic slow time scale and a periodic fast time scale. Circuits driven by envelope-modulated signals, in which the baseband signal (the information) is aperiodic and has a spectral content of much lower frequency than the periodic carrier, are typical examples of practical interest involving such time evolution rates. The discussed method is tailored to take advantage of the circuits and signals heterogeneity and so will benefit from the time-domain latency of some state variables in the circuits. Because the aperiodic slowly varying state variables are treated only in time domain, the proposed method can be seen as a hybrid scheme combining multitime envelope transient harmonic balance based on a multivariate formulation, with a purely time-step integration scheme.

This paper reviews some of the promising doors that functional analysis techniques have recently opened in the field of electronic circuit simulation. Because of the modulated nature of radio frequency (RF) signals, the corresponding electronic circuits seem to operate in a slow time scale for the aperiodic information and another, much faster, time scale for the periodic carrier. This apparent multirate behavior can be appropriately described using partial differential equations (PDEs) within a bivariate framework, which can be solved in an efficient way using hybrid time-frequency techniques. With these techniques, the aperiodic information dimension is treated in the discrete time domain, while the periodic carrier dimension is processed in the frequency domain, in which the solution is evaluated within a space of harmonically related sinusoidal functions. The objective of this paper is thus to provide a general overview on the most important hybrid time-frequency techniques, as the ones found in commercial tools or the ones recently published in the literature.

This paper presents a method for extracting MFCC parameters from a normalised power spectrum density. The underlined spectral normalisation method is based on the fact that the speech regions with less energy need more robustness, since in these regions the noise is more dominant, thus the speech is more corrupted. Less energy speech regions contain usually sounds of unvoiced nature where are included nearly half of the consonants, and are by nature the least reliable ones due to the effective noise presence even when the speech is acquired under controlled conditions. This spectral normalisation was tested under additive artificial white noise in an Isolated Speech Recogniser and showed very promising results [1]. It is well known that concerned to speech representation, MFCC parameters appear to be more effective than power spectrum based features. This paper shows how the cepstral speech representation can take advantage of the above-referred spectral normalisation and shows some results in the continuous speech recognition paradigm in clean and artificial noise conditions.

Independent Component Analysis (ICA) is a statistical based method, which goal is to find a linear transformation to apply to an observed multidimensional random vector such that its components become as statistically independent from each other as possible. Usually the Electroencephalographic (EEG) signal is hard to interpret and analyse since it is corrupted by some artifacts which originates the rejection of contaminated segments and perhaps in an unacceptable loss of data. The ICA filters trained on data collected during EEG sessions can identify statistically independent source channels which could then be further processed by using event-related potential (ERP), event-related spectral perturbation (ERSP) or other signal processing techniques. This paper describes, as a preliminary work, the application of ICA to EEG recordings of the human brain activity, showing its applicability.

This paper is concerned to the noisy speech HMM modelling when the noise is additive, speech independent and the spectral analysis is based on sub-bands. The internal distributions of the noisy speech HMM’s were derived when Gaussian mixture density distributions for clean speech HMM modelling are used, and the noise is normally distributed and additive in the time domain. In these circumstances it is showed that the HMM noisy speech distributions are not Gaussians, however, fitting these distributions as a Gaussian mixture, only a little bit of loss in performance was obtained at very low signal to noise ratios, when compared with the case where the real distributions were computed using Monte Carlo methods.

The changing on peaks structure of the speech spectrum is perhaps the most important cause of degradation of speech recognition systems under adverse conditions. Another drawback concerned to the additive noise effect occurs on the flat spectral zones which are usually raised proportionally to the noise level. These combined effects on both the peaked and the flat spectral zones can be alleviated by trying to restore its original structure, which assumes noise knowledge. However, the random nature and the variability of the noise, the difficulty in discriminating speech pauses, among others, discourage the use of noise estimates as the basis of robust speech recognition algorithms. Alternative approaches based on normalisation procedures become very promising since the noise effect can be alleviated without any knowledge regarding to its existence. This paper suggests a spectral normalisation that though being different can be viewed as a noise estimation procedure in a frame by frame basis, so assuming the clean database as lightly corrupted. This speech normalisation is used to restore the normalised speech spectrum. This normalised spectrum is then re-normalised by a baseline spectrum normalisation method, which concentrates essentially in the speech regions of small energy, since in these regions the noise is more dominant, so they require a better degree of robustness.