C.S. Lindquist

Radial basis function transforms and their use in signal processing

A variety of standard basis functions have long been used for characterizing signals including Fourier, Walsh, Haar, and Slant. Optimum Karhunen-Loeve basis functions derived from correlation data can also be used. Radial basis functions are a new type. They are based on actual data rather than predefined or generated sets. This paper relates radial basis functions and standard basis functions. It reviews how they are derived and illustrates their broad use with EKG and stock market examples. They have great utility and may become as common as their standard predecessors.<<ETX>>

Design of demodulators using time-varying adaptive digital filters

A discussion is presented of the design of time-varying adaptive digital filters used for amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase-shift keying (PSK) demodulation in communication systems. It is shown that these time-varying time domain algorithms require less computations and hence are more efficient than frequency domain algorithms. An efficient inversion technique is exploited in these time domain formulations. Simulations are presented and discussed.<<ETX>>

Use of adaptive segmentation and classification algorithms in satellite imagery

Use of satellite imagery continues to grow. Development of DSP algorithms for automated analysis is therefore becoming increasingly important. Areas of immediate application are diverse such as agriculture, deforestation, soil erosion, etc. This paper presents adaptive edge algorithms which identify region boundaries and pattern recognition algorithms to classify the regions within these boundaries. An illustrative example using a satellite image of an agricultural area is presented to demonstrate these algorithms.

The use of data profiles in class 2 and 3 adaptive filters

Adaptive filters are optimum filters whose transfer functions adapt to changing input statistics. Such adaptation is usually needed because of fluctuating signal and/or noise conditions. These filters can be classified in order of increasing difficulty based upon the a priori assumptions about the signal and noise models. A class 2/3 adaptive filter is a transitional filter between class 2 and class 3 filters. In this paper, we use data profiles to formulate class 2/3 filters. Averaging provides an estimate of the signal and eliminates noise. Data profiles can also be used to formulate either class 2 and/or class 3 filters. Results show that this method provides improved estimates of expected signal and/or noise by smoothing the average signal profile. To demonstrate this approach, these results are used to process EKG signals where no a priori information is available.<<ETX>>

Adaptive filter design for estimation and detection of biological signals: an application to electroencephalography

An innovative technique for estimation and detection of alpha waves using adaptive filters is presented. In these analyses both Wiener transfer functions and non-Wiener transfer functions are used. Comparisons are made for different RMS signal-to-noise ratios. Simulations are done with class 1 filters where prior knowledge of all spectra estimates is assumed. These techniques are found to be very flexible in their application to other biological signals.<<ETX>>This paper presents an innovative technique for estimation and detection of alpha waves using adaptive filters. In these analyses both Wiener transfer functions and non-Wiener transfer functions were used. Comparisons were made for different SNRrms. These techniques were found to be very flexible in their application to other biological signals.

Image processing using adaptive aposteriori Wiener estimation techniques

We describe the generalized, two-dimensional Wiener estimation algorithm in the frequency domain. An adaptive aposteriori estimation technique is then presented. The technique is applied to a specific example and results are illustrated.<<ETX>>

Nomographs for MFMBO filters (maximally flat magnitude beyond the origin)

Filter nomographs have proven to be effective design tools in determining filter order and evaluating design tradeoffs. This paper presents nomographs for filters that are maximally flat magnitude beyond the origin (MFMBO). It is shown that MFMBO filters display transitional characteristics and can be designed for different shaping factors. The proposed nomographs con be used to determine filter order and degrees of freedom in a MFMBO filter design.

Selection of transforms including radial basis functions in class 1 filters

Class 1 filters utilize expected signal, noise, and their correlations to form estimation, detection, correlation, and other types of algorithms. The authors discuss the selection of transforms including radial basis functions in Class 1 filters. These results are used to process EKG signals and demonstrate that transforms and filters must be properly matched.

Use of smoothing in class 1 frequency domain estimation matrix filters

It is observed that the performance of the frequency-domain Wiener estimation filters relies heavily on the type of smoothing algorithm and the characteristics of the signal. Thus, the designer or engineer must carefully select the optimum system regarding the implementation domain, smoothing algorithm, and computation complexity. Simulations showed that a frequency-domain Wiener estimation filter using diagonal smoothing perfectly estimates a narrowband signal. On the other hand, circulant smoothing is proved to be superior when estimating wideband signals. Both Toeplitz and circulant smoothing perform well for time-limited signals, thus necessitating a tradeoff between vector sparseness and MSE. It was found that diagonal smoothing yields the most computationally efficient structure. Therefore, advantage must be taken of this fact; for example, if the Fourier transformation is used, filters performing well under frequency-domain circulant smoothing can be replaced with time-domain filters using diagonal smoothing techniques.<<ETX>>

New image processing algorithms requiring almost no a priori design information

New Class 3 image processing algorithms are presented. They are direct extensions of previously published one-dimensional algorithms. Class 3 algorithms require almost no a priori information knowledge about the signal and noise that are being processed. Their performance depends upon the kind of smoothing used and on the images being processed by the filter. The previously published Class 3 filter algorithms require that the filter input be stationary, and that the noise spectrum have zero mean and be uncorrelated to the signal. For the new Class 3 image processing algorithms, the only additional assumption for the noise is that its spectrum be white. Simulations using Lena demonstrate much better performance using the new Class 3 algorithms over the standard Class 3 algorithms.