A flexible and computationally efficient method for spectral analysis of sinusoidal signals using the Basis Pursuit De-Noising (BPDN) is proposed. This method estimates a slotted Auto-Correlation Function (ACF) and computes the spectrum as the sparse representation of the ACF in a dictionary of cosine functions. Simulation results illustrate flexibility and effectiveness of the proposed method.

An improvement of estimating sound power spectra located in a particular 2-dimensional area is proposed. We previously proposed a conventional method that estimates sound power spectra using multiple fixed beamformings in order to emphasize speech located in a particular 2-dimensional area. However, the method has one drawback that the number of areas where the active sound sources are located must be restricted. This restriction makes the method less effective when many noise source located in different areas are simultaneously active. In this paper, we reveal the cause of this restriction and determine the maximum number of areas for which the method is able to simultaneously estimate sound power spectra. Then we also introduce a procedure for investigating areas that include active sound sources to reduce the number of unknown power spectra to be estimated. The effectiveness of the proposed method is examined by experimental evaluation applied to sounds recorded in a practical environment.

A method for extracting a sound signal from a particular area that is surrounded by multiple ambient noise sources is proposed. This method performs several fixed beamformings on a pair of small microphone arrays separated from each other to estimate the signal and noise power spectra. Noise suppression is achieved by applying spectrum emphasis to the output of fixed beamforming in the frequency domain, which is derived from the estimated power spectra. In experiments performed in a room with reverberation, this method succeeded in suppressing the ambient noise, giving an SNR improvement of more than 10 dB, which is better than the performance of the conventional fixed and adaptive beamforming methods using a large-aperture microphone array. We also confirmed that this method keeps its performance even if the noise source location changes continuously or abruptly.

High-resolution spectrum estimation techniques have been extensively studied in recent publications. Knowledge of the noise variance is vital for spectrum estimation from noise-corrupted observations. This paper presents the use of noise compensation and data extrapolation for spectrum estimation. We assume that the observed data sequence can be represented by a set of autoregressive parameters. A recently proposed iterative algorithm is then used for noise variance estimation while autoregressive parameters are used for data extrapolation. We also present analytical results to show the exponential decay characteristics of the extrapolated samples and the frequency domain smoothing effect of data extrapolation. Some statistical results are also derived. The proposed noise-compensated data extrapolation approach is applied to both the autoregressive and FFT-based spectrum estimation methods. Finally, simulation results show the superiority of the method in terms of bias reduction and resolution improvement for sinusoids buried in noise.

We present a new method for estimation of spectrum transition of nonstationary signals in cases of low signal-to-noise ratio (SNR). Instead of the basic functions employed in the previously proposed time-varying autoregressive (AR) modeling, we introduce a spectrum transition constraint into the cost function described by the partial correlation (PARCORR) coefficients so that the method is applicable to noisy nonstationary signals of which spectrum transition patterns are complex. By applying this method to the analysis of vibration signals on the interventricular septum (IVS) of the heart, noninvasively measured by the novel method developed in our laboratory using ultrasonics, the spectrum transition pattern is clearly obtained during one cardiac cycle for normal subjects and a patient with cardiomyopathy.

This paper proposes a nonlinear signal processing by using a three layered network which is trained with self-organized clustering and supervised learning. The network consists of three layers, i.e., self-organized layer, an evaluation layer and an output layer. Since the evaluation layer is designed as a simple perceptron network and the output layer is designed as a fixed weight linear node, the training complexity is the same as a conventional one consisting of self-organized clustering and a simple perceptron network. In other words, quite high speed training can be realized. Generally speaking, since the data range is arbitrary large in signal procession, the network shoulk cover this range and output a value as accurately as possible. However, it may be hard for only a node in the network to output these data. Instead of this mechanism, if this dynamic range is covered by using several nodes, the complexity of each node is reduced and the associated range is also limited. This results on the higher performance of the network than conventional RBFs. This paper introduces a new non-linear spectrum estimation which consists of LPC analysis and RBF network. It is shown that accuracy spectrum envelopes can be obtained since a new RBF network can estimate some nonlinearities in a speech production.

We present a new method to cancel interfering sinusoidal signals. In this method, the Interpolated FFT (IpFFT) algorithm is used to estimate the parameters of the interference signal: frequency, amplitude and phase. The cancellation is then performed in the time domain. In order for the IpFFT to perform reliably, accurate spectral information about the interference signal is needed. Since, the information signal masks the interference signal, it becomes difficult to estimate the parameters of the interference signal. To alleviate this masking effect, two techniques are discussed here. These techniques involve frame update of interference spectral information of the interference signal, and adaptive averaging. Significant improvement over conventional frequency domain filterings is achieved. The price paid is only little, beyond the computation of the FFT. Comparison with the conventional frequency domain filter shows that our system has approximately 5dB better cancellation capability for a single interfering signal.