WINDOWS: Finite Aperture Effects and Applications in Signal Processing
by fred j. harris

A window is the aperture through we examine the world. By necessity, any time or spatial signal we observe, collect, and process must have bounded support. Similarly, any time or spatial signal we approximate, design, and synthesize must also have bounded support. Support is the range or width of the independent variable (time, distance, or frequency) over which the dependent variable, say the signal, is non-zero. This finite support can be defined over multiple dimensions, extending for instance, over a line, a plane, or a volume. Windows can be continuous functions or discrete sequences defined over their appropriate finite supports.
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Adaptive Filters Using Fractal Dimension of Data
by fred j. harris, Deborah S. Kin

The fractal dimension of a data series can be used as a sensitive indicator of the temporal variability of a signal. Smooth continuous signals have fractal dimension of one while signals with discontinuities and very noisy signals have fractal dimension between one and two. This measure, estimated over short sliding intervals, can be used to adjust the local spectral characteristics of a digital filter to emphasize or to suppress local temporal features of the signal. We have examined and have compared the performance of a number of filters with parameters controlled by the short term fractal dimension of two classes of signals. The processed signals were sinusoids and square waves with varying amounts of additive white Gaussian noise. The filter structures included the finite impulse response (FIR), infinite impulse response (IIR), and edian filters. We examined two methods of changing the filters with fractal dimension; these were, changing between fixed filters as the fractal dimension crossed thresholds, and changing filter parameters proportionally with the fractal dimension. In addition to describing the filtering process we also report on methods for estimating the fractal dimension over the sliding Interval.
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Teaching MODEM Concepts and Design Procedure with MATLAB Simulations
by fred j. harris

MATLAB simulation is used as the primary tool to illustrate concepts, to validate MODEM designs, and to vent' operation of the subsystems employed in DSP based transmitters and receivers presented in a pair of classes on MODEM Design and Digital Receiver Design. The whole gamut of subsystems found in conventional and experimental modem designs are simulated and assembled to form a full end-to-end simulation of an operating MODEM. This paper describes the philosophy used to guide class involvement and assess the experience and the learning value to student participants.
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High Resolution Spectral Methods in SAR and ISAR Processing
by fred j. harris

We show that by proper perspective the polar format processing for high resolution radar imaging can be viewed as the spectral description of the focusing required for standard range and cross-range processing. Alternatively we can show that range and cross-range processing is simply a first order approximation to polar format processing. In this light we also demonstrate a number of simple to implement (focusing) transformations to effect partial polar mapping and thus obtain imaging performance between that of the two imaging techniques.
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Performance and Design of Farrow Filter Used For Arbitrary Resampling
by fred j. harris

The Farrow filter is a multirate filter structure which offers the option of continuously adjustable resample ratio. This paper presents a derivation of the method proposed by Farrow, and demonstrates the performance and complexity of resampling filters using his technique. The paper also develops some important system options made available to the designer as spin-offs of the derivation.
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