The sliding discrete Fourier transform (DFT) is a well-known algorithm for obtaining a few frequency components of the DFT spectrum with a low computational cost. However, the conventional sliding DFT cannot be applied to practical conditions, e.g., using the sine window and the zero-padding DFT, with preserving the computational efficiency. This paper discusses the extension of the sliding DFT to such cases. Expressing the window function by complex sinusoids, a recursive algorithm for computing a frequency component of the DFT spectrum using an arbitrary sinusoidal window function is derived. The algorithm can be easily extended to the zero-padding DFT. Computer simulations using very long signals show the validity of our algorithm.

An algorithm for blind signal separation (BSS) of convolutive mixtures is presented. In this algorithm, the BSS problem is treated as multidimensional independent component analysis (ICA) by introducing an extended signal vector which is composed of current and previous samples of signals. It is empirically known that a number of conventional ICA algorithms solve the multidimensional ICA problem up to permutation and scaling of signals. In this paper, we give theoretical justification for using any conventional ICA algorithm. Then, we discuss the remaining problems, i.e., permutation and scaling of signals. To solve the permutation problem, we propose a simple algorithm which classifies the signals obtained by a conventional ICA algorithm into mutually independent subsets by utilizing temporal structure of the signals. For the scaling problem, we prove that the method proposed by Koldovský and Tichavský is theoretically proper in respect of estimating filtered versions of source signals which are observed at sensors.

A method for measuring similarity between two variables is presented. Our approach considers the case where available observations are arbitrarily filtered versions of the variables. In order to measure the similarity between the original variables from the observations, we propose an error-minimizing filter (EMF). The EMF is designed so that an error between outputs of the EMF is minimized. In this paper, the EMF is constructed by a finite impulse response (FIR) filter, and the error between the outputs is evaluated by the mean square error (EMF). We show that minimization of the MSE results in an eigenvalue problem, and the optimal solution is given in a closed form. We also reveal that the minimal MSE by the EMF is efficient in the measurement of the similarity from the viewpoint of a correlation coefficient between the originals.

In this paper, we present update rules for convolutive nonnegative matrix factorization (NMF) in which cost functions are based on the squared Euclidean distance, the Kullback-Leibler (KL) divergence and the Itakura-Saito (IS) divergence. We define an auxiliary function for each cost function and derive the update rule. We also apply this method to the single-channel signal separation in speech signals. Experimental results showed that the convergence of our KL divergence-based method was better than that in the conventional method, and our method achieved single-channel signal separation successfully.

The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.

This paper proposes a private communication system with chaos using fixed-point digital computation. When fixed-point computation is adopted, chaotic properties of the modulated signal should be checked carefully as well as calculation error problems (especially, overflow problems). In this paper, we propose a novel chaos modem system for private communications including a chaotic neuron type nonlinearity, an unstable digital filter and an overflow function. We demonstrate that the modulated signal reveals hyperchaotic property within 10,000 data point fixed-point computation, and evaluate the security of this system in view of the sensitivity of coefficients for demodulation.

The conventional linear prediction can be viewed as a constrained blind equalization problem that has gained a lot of interests along with development of telecommunication networks. Because the blind equalization or deconvolution is a general framework of the inverse problem, the reliable and faster algorithm is requested in many applications. This paper proposes an orthogonal wavelet transform domain realization of a blind equalization technique termed as EVA, and presents an application to speech analysis. An orthogonal transformation has no influence to the equalization result in general, but we show that a particular wavelet makes the matrix in EVA nearly lower triangular that promotes the faster convergence in the estimation of maximum eigenvalue and its associate vector in EVA iteration. The experiments with the Japanese vowels show that the the proposed method effectively separates the glottis and vocal tract information, hence is promising for speech analysis.

This paper describes a new method of approximating ideal Hilbert transformers by using time reversal techniques. As is well known, an ideal Hilbert transformer is not physically realizable because it is not causal. Nevertheless, it is extremely imprortant conceptually in the area of digital signal processing. In this paper, we propose a method to approximately implement such a Hilbert transformer. The method divides the impulse response of the ideal Hilbert transformer into two parts, i.e., causal and noncausal parts. Although a causal filter is physically realizable, a noncausal filter is not realizable. A noncausal filter is realized using time reversal techniques for input signals to the filter, and then the Hilbert transformer can be approximately implemented by the parallel connection of causal and noncausal filters.

An algorithm for estimating sinusoidal parameters is presented. In this paper, it is assumed that an observed signal is a single sinusoidal signal contaminated by white Gaussian noise. Based on this assumption, the sinusoidal parameters can be found by minimizing a cost function using the mean squared error (MSE) between the observed signal and a sinusoidal signal with arbitrary sinusoidal parameters. Because the cost function is nonlinear and not convex, it has undesirable local minima. To solve the minimization problem, we propose to use the roots of an algebraic equation. The algebraic equation is derived straightforwardly from the cost function. We show that the global solution is formulated by using the roots of the algebraic equation.

This paper presents a novel algorithm for spectral subtraction (SS). The method is derived from a relation between the spectrum obtained by the discrete Fourier transform (DFT) and that by a subspace decomposition method. By using the relation, it is shown that a noise reduction algorithm based on subspace decomposition is led to an SS method in which noise components in an observed signal are eliminated by subtracting variance of noise process in the frequency domain. Moreover, it is shown that the method can significantly reduce computational complexity in comparison with the method based on the standard subspace decomposition. In a similar manner to the conventional SS methods, our method also exploits the variance of noise process estimated from a preceding segment where speech is absent, whereas the noise is present. In order to more reliably detect such non-speech segments, a novel robust voice activity detector (VAD) is then proposed. The VAD utilizes the spread of eigenvalues of an autocorrelation matrix corresponding to the observed signal. Simulation results show that the proposed method yields an improved enhancement quality in comparison with the conventional SS based schemes.