Data processing: artificial intelligence – Fuzzy logic hardware
Reexamination Certificate
1997-12-09
2001-12-18
Powell, Mark (Department: 2122)
Data processing: artificial intelligence
Fuzzy logic hardware
C084S626000
Reexamination Certificate
active
06332136
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a fuzzy filtering method and associated fuzzy filter.
2. Discussion of the Related Art
As is known, a large number of mass-market applications (such as hi-fi, telecommunications) requires the definition of dedicated methods and architectures for filtering the deterministic signals corrupted by noise.
Traditionally, the problems of noise reduction (“denoising”) are dealt with using linear filters (such as low-pass type filters with a fixed cut-off frequency) or with non-linear filters such as median filters.
The traditional linear filters are ideal for solving problems in which the frequency specifications are well defined. They do, however, have the disadvantage that, to reduce noise, they often eliminate data belonging to the original signal. As far as non-linear type filters are concerned, median filters have proved to be very efficient in eliminating pulse-type noise, but they are less efficient in the case of Gaussian noise.
For this reason, filters of a completely different type have been proposed: for instance, the article entitled “Fuzzy Rule-Based Signal Processing and Its Application to Image Restoration” by Kaoru Arakawa, IEEE Journal on Selected Areas in Communications, Vol. 12, No. 9, December 94, proposes a filter based on the processing of the signal by means of “fuzzy” logic, in which the signal is reconstructed by means of a filter which weighs local samples of the signal received and the weights are calculated using three rules whose variables are the difference between the signal samples, the time difference between those signal samples and the local variance of the signal. The filter also uses a learning signal to fix a number of filtering parameters.
This approach is burdensome in its calculations and is not always capable of supplying the desired accuracy of reconstruction of the signal.
SUMMARY OF THE INVENTION
An object of the invention is therefore to provide a method and a filter for signals affected by noise, in particular by white noise of Gaussian distribution, which is capable of performing an efficient reconstruction of the signal, with calculation work that is reduced or in any event acceptable as regards the intended applications.
According to one aspect of the invention, a fuzzy filtering method and associated fuzzy filter are provided. In practice, according to one aspect of the invention, the filtering is carried out by using, as variables, the variation of the signal in the considered window and the distance between the samples and a sample to be reconstructed. This distinguishes the typical variations of the original signal from those due to the noise, and allows an identification of the signal fronts.
According to one embodiment of the invention, a method of fuzzy filtering of a noise signal comprising a plurality of signal samples is disclosed, the method comprising the steps of: a) defining a current signal sample from among the plurality of signal samples, b) calculating a plurality of difference samples as the difference in absolute value between the current signal sample and each sample of the plurality of signal samples, c) defining distance values between the current signal sample and each sample of the plurality of signal samples, d) determining weight parameters on the basis of the difference samples and the distance values by means of fuzzy logic and e) weighing the signal samples with the weight parameters so as to obtain a reconstructed current signal sample.
The method further comprises the steps of: f) calculating a noise sample as the difference between the reconstructed current signal sample and the current signal sample, repeating steps (a)-(f) to obtain a plurality of reconstructed current signal samples and a plurality of noise samples, determining a noise maximum variation value on the basis of a maximum value and a minimum value of the noise samples, determining a signal maximum variation value on the basis of a maximum value and a minimum value of the signal samples and determining at least two first classes of membership for the plurality of difference samples, the first classes of membership being defined by functions with sections having as limits the noise and signal maximum variation values. The method comprises associating with each difference sample a respective difference level of truth in each of the first classes of membership; determining at least two second classes of membership for the distance values, associating with each distance value a respective distance level of truth in each of the second classes of membership, applying fuzzy rules to associate the difference and distance levels of truth with weight values and with respective third classes of membership and determining the weight parameters as a function of the weight values and with pre-determined parameters of the third classes of membership.
The step of determining at least two first classes of membership comprises the steps of determining a SMALL membership class having a horizontal section for values of the difference samples between zero and the noise maximum variation value and a section of constant gradient for values of the difference samples between the noise maximum variation value and the signal maximum variation value, determining a LARGE membership limitation value as the difference between the signal maximum variation value and the noise maximum variation value and determining a LARGE membership class having a constant gradient section for values of the difference samples between zero and the LARGE membership limitation value and a horizontal section for values of the difference samples between the LARGE membership limitation value and the signal maximum variation value.
The step of associating with each difference sample comprises the steps of:
i. determining a central point of the constant gradient sections of the SMALL and LARGE membership classes;
ii. setting the difference level of truth equal to a pre-determined value;
iii. comparing the difference sample with the central point;
iv. determining a comparison point on the left of the central point if the difference sample is less than the central point and a comparison point on the right of the central point if the difference sample is greater than the central point;
v. comparing the difference sample with the comparison point;
vi. if the difference sample is less than the comparison point on the left, modifying the difference level of truth according to a first direction of increment and modifying the comparison point on the left; or
vii. if the difference sample is greater than the comparison point on the right, modifying the difference level of truth according to a second direction of increment and modifying the comparison point on the right; and
viii. repeating the steps v. and vi. or vii. until the difference sample is greater than the comparison point on the left or less than the comparison point on the right.
The method determines a sub-interval width of the constant gradient sections equal to the width of the constant gradient sections divided by a power of 2. The step of modifying the comparison point on the left comprises the step of decrementing the comparison point on the left by a quantity equal to the sub-interval width and wherein the step of modifying the comparison point on the right comprises the step of incrementing the comparison point on the right by a quantity equal to the sub-interval width.
According to another embodiment of the invention, a filter for implementing fuzzy filtering is disclosed. The filter comprises first store means for storing signal samples, second store means for storing noise samples, third store means for storing difference samples, subtractor means connected to the first and second store means, maximum/minimum value determination means connected to the first and second store means. The filter further comprises fourth store means for storing minimum and maximum values of signal samples and of noise samples, the fourth store means being connected to the su
Di Giura Maddalena
Pagni Andrea
Poluzzi Rinaldo
Rizzotto Gianguido
Galanthay Theodore E.
Morris James H.
Powell Mark
SGS--Thomson Microelectronics S.r.l.
Starks Wilbert
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