A class of finite-impulse response (FIR) median hybrid (FMH) filters that contain linear FIR substructures to estimate the current signal value using forward and backward prediction is introduced. The output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window. Predictors maximizing the signal-to-noise ratio on signal sections described by an lth-order polynominal are derived. The ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the standard median (SM) filters. The new predictive FMH filters are shown to have root signals which do not exist for the SM filters, e.g. triangular waves. By combining the level and the ramp enhancement FMH filters, a filter is obtained which attenuates noise on constant and ramp signals. The noise attenuation on ramp signals is better than with the SM filter, and the predictive FMH filter has novel and meaningful root structures. The number of arithmetic operations needed to implement the predictive FMH filter grows linearly with the length of the filter. >

FIR-median hybrid filters with predictive FIR substructures

New families of finite-impulse-response (FIR) digital filters with low computational complexity are presented. The filters are extensions of the recursive running sum. Each family of filters predicts points along a characteristic polynomial. Closed-form equations are given in both time- and frequency-domain for filters corresponding to first- and second-order polynomial models. Block diagrams for efficient implementation structures are given. The first-order predictive filters require three multipliers and five adders, and the second-order predictive filters require five multipliers and twelve adders, irrespective of the filter length. The filters exhibit low-pass characteristics with the passband shape controllable by a single parameter. The frequency and phase responses are discussed. A design example is given showing how the filters can be used as building blocks to obtain effective linear-phase low-pass filters. >

Predictive FIR filters with low computational complexity

Two classes of FIR-median hybrid (FMH) filters are introduced, which are called in-place growing FIR-median hybrid (IPG-FMH) and recursive in-place growing FIR-median hybrid (RIPG-FMH) filters. This new extended family of filters exhibits a very small bias error in the vicinity of an edge, an yet provides good noise attenuation. It is shown that the IPG-FMH filters can be expressed as weighted FMH (WFMH) filters. >

FIR-median hybrid filters with excellent transient response in noisy conditions

A sorter-based processor architecture is introduced for digital signal processing purposes. The processor has been optimized to implement sliding average-type linear structures and three- and five-sample sorting operations. The specialized processor can be used, for example, for the several variations of the finite-impulse-response (FIR) median hybrid (FMH) filters, as well as other types of ranked-order filters and running-sum averaging operations. FMH filters with averaging substructures and window lengths of up to 65 samples can be computed with sampling intervals of less than 20 clock cycles. The 12-bit microprogrammable core processor is designed as a full-custom very large scale integration (VLSI) circuit. Examples of filter implementations show that the sorter-based processor architecture is suitable for several kinds of digital signal processing tasks. >

A signal processor for median-based algorithms

A class of nonlinear filters that are based on the rank estimates (R-estimates) of location parameters in statistical theory is introduced. It is shown how moving-window rank filters (R-filters) can be defined starting from rank estimates of location. These filters utilize the relative ranks of the observations in each window to produce an output value. The idea of rank Winsorization is extended to that of averaging only observations which lie within small temporal neighborhoods. This leads to a definition of the class of generalized Wilcoxon (GW) filters, which are parameterized by three parameters, namely the degrees of temporal and rank Winsorization and the degree of averaging. The GW filters can be defined to have desirable characteristics of edge preservation, detail retention, and impulse rejection, in addition to the property of Gaussian noise smoothing. Performance characteristics of these filters are considered through analysis and simulation. The filters show that all three well-known classes of robust location estimates, the L-, M-, and R-estimates, can be applied to nonlinear smoothing of signals. >

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Nonlinear smoothing filters based on rank estimates of location

In this paper, we introduce a new class of FIR Median Hybrid (FMH) filters which contain linear FIR substructures to estimate the current signal value using forward and backward prediction The output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window Predictors maximizing the signal to noise ratio on signal sections described by an 1th order polynomial are derived The ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the Standard Median (SM) filters The new predictive FMH filters are shown to have root signals which do not exist for the SM filters, eg triangular waves By combining the level and the ramp enhancement FMH filters, we obtain a filter which attenuates noise on constant and ramp signals

Y. Neuvo

Papers

Median type filters with linear predictive substructures