Pattern recognition is a very powerful tool in automated data analysis and it is widely used in many different applications (Chou & Juang, 2003; Jiang,1994; Blue et al., 1994; Milosavljevic, 1994; Moreels & Smrekar, 2003). However, the application of such a tool can be a difficult task in some cases. For example, in a correlation-type scheme, the basic idea is to correlate the signal being analyzed with a known template or templates (Shiavi, 1999; Scharf, 1991) and make decisions based on the magnitude of the correlation coefficients, which is between 0 and 1. In practice, these extreme values are seldom achieved due to corrupting signals/noise that can affect the accuracy of pattern matching and subsequently lead to errors in classification (Kil & Shin, 1996). The corrupting signals may also bear some resemblance to the template being matched. This is particularly true if the pattern of interest is a non-stationary transient signal. Furthermore, it is well known that traditional time domain correlation-based pattern recognition methods do not fully utilize the frequency characteristics of the template and the signal being analyzed. Hence, such methods perform poorly when applied to transient signals. To overcome these difficulties, a scheme known as selective regional correlation (SRC) has been developed (Sejdic & Jiang, 2007). It has been shown that if a template has bandlimited characteristics, significant improvement in the performance of pattern recognition can be readily made by a relatively simple preprocessing of the signal and the template in the time-frequency domain (Sejdic & Jiang, 2007). The redundant representation of a 1D signal in a 2D time-frequency domain can provide an additional degree of freedom for signal analysis. Such pre-processing effectively separates the intertwined time domain features of the signal, allowing the important characteristics to be exposed in the time-frequency domain, resulting in more effective pattern matching. Hence, correlation between the signal being analyzed and the template needs to be conducted only in selected regions of interest in the time-frequency domain. An overview of the theoretical developments behind the SRC is provided in this chapter along with some recent results. The performance of the scheme is briefly reviewed and compared with that of the general correlation technique through the analysis of a set of O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Instantaneous frequency (IF) estimation through the estimation of peak locations in the time-frequency plane is an important approach for signals contaminated with additive white Gaussian noise. In this paper, the forementioned analysis is carried out for continuous wavelet transform. The analysis of the scalogram as the instantaneous frequency estimator is performed for any FM signal regardless of the mother wavelet. Accurate expressions for the bias and the variance of the estimator are derived, and reveal that the bias and the variance are signal dependent. Results are statistically confirmed through the numerical analysis for several mother wavelets, and among considered wavelets, the Morlet wavelet produces the smallest estimation error. Furthermore, the performance of the IF estimator based on the scalogram and the spectrogram were compared through analysis of mean square error. These results showed that the scalogram with the Morlet wavelet exhibited good performance for the sample linear FM signal and the sample hyperbolic FM signal in comparison to the spectrogram.

Accurate and sparse representation of a moderately fast fading channel using bases functions is achievable when both channel and bases bands align. If a mismatch exists, usually a larger number of bases functions is needed to achieve the same accuracy. In this paper, we propose a novel approach for channel estimation based on frames, which preserves sparsity and improves estimation accuracy. Members of the frame are formed by modulating and varying the bandwidth of discrete prolate spheroidal sequences (DPSS) in order to reflect various scattering scenarios. To achieve the sparsity of the proposed representation, a matching pursuit approach is employed. The estimation accuracy of the scheme is evaluated and compared with the accuracy of a Slepian basis expansion estimator based on DPSS for a variety of mobile channel parameters. The results clearly indicate that for the same number of atoms, a significantly higher estimation accuracy is achievable with the proposed scheme when compared to the DPSS estimator.

We present a non-invasive brain-machine-interface (BMI) prototype system which allows the simple control of a switch. The main goal of the system, based on electroencephalogram (EEG) recordings, is to create mechanical action from brain activity. Experimental work presented in this paper outlines the operation of a system which is a crude imitation of an ultrasound echolocation based vision mechanism, commonly used by bats and dolphins, which is controlled by brain activity. Simple time-frequency-space domain signal analysis methods are employed to generate the electrical control-signal, while the sonar transducer is mounted on a robotic arm capable of scanning the upper hemisphere.

Instantaneous frequency (IF) is a fundamental concept that can be found in many disciplines such as communications, speech, and music processing. In this letter, analysis of an IF estimator, based on a time-frequency technique known as S-transform, is performed. The performance analysis is carried out in a white Gaussian noise environment, and expressions for the bias and the variance of the estimator are determined. The results show that the bias and the variance are signal dependent. This has been statistically confirmed through numerical simulations of several signal classes.

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.

Clinical experience has shown that heart sounds can be an effective tool to noninvasively diagnose some forms of heart disease. In this paper, an algorithm based on time-frequency analysis is used for the decomposition of the heart sounds. The decomposition algorithm is based on the S-method. The S-method is a time-frequency representation that can produce a distribution equal or close to the sum of the Wigner distributions of individual signal components. The decomposition algorithm is used for segmentation of the heart sound recordings that contain either of the two sounds: opening snap or third heart sound, which indicate distinct heart diseases. The results show that the algorithm effectively decomposes each heart beat into the corresponding components. Hence, they may be used in conjunction with a classification algorithm, allowing automatic decomposition and classification of the heart diseases associated with the opening snap and the third heart sound.

A time-frequency signal analysis tool, known as S-transform, can suffer from poor energy concentration in the time-frequency domain. In this paper, a frequency dependent Kaiser window is presented for improving the energy concentration of the S-transform. The new window is analyzed using a set of test signals. The results indicate that the proposed scheme can significantly improve the energy concentration in the time-frequency domain in comparison with the standard S-transform.

In this paper, a novel correlation-based pattern classifier that relies on the analysis of time-frequency decomposition of a template and signals is proposed. Significant improvements in resolution and accuracy are obtained using this new classifier when compared to a conventional correlation-based one. The short-time Fourier transform, continuous wavelet transform, and S-transform are considered in the time-frequency decomposition process. To evaluate the performance of the proposed scheme, numerical studies are performed on a set of synthetic test signals, and excellent results have been obtained. This paper also presents an illustrative example where two types of heart sounds are classified. The classification error percentage for the heart sounds using the new classifier is only 6.670% as compared to 56.67% when a general correlation-based classifier is used

In this paper, it is demonstrated that time-frequency techniques may be used for an enhanced diagnosis of the heart disease. Three time-frequency analysis techniques are compared: spectrogram, Wigner distribution and S- method. The results show that the S-method could be used in the heart sounds analysis, and that is also capable of enhancing the diagnostic techniques available to medical personnel.

The effect of three time-frequency representations on a novel correlation algorithm is studied. By representing a signal in the time-frequency domain, a redundant representation of the signal is obtained. The algorithm presented relies on such redundancies to extrapolate some significant features of the signal. The developed scheme has been applied to heart sound analysis using real recordings from patients, where the opening snap (OS) is distinguished from the third heart sound (S3). The results for the three time-frequency transforms are compared and very encouraging results have been obtained with S-transform.