RU2400809C1 - Digital filter for assessment of slowly changing median of signal - Google Patents

Abstract

FIELD: information technologies. ^ SUBSTANCE: invention relates to specialised computer means and may be used in systems, where hardware implementation of algorithms of digital signal filtration is required. For instance, when zero level is assessed at the background of pulse signals/noise or under conditions of asymmetrical limitation of dynamic range, relative to zero level. Digital filter comprises digital comparator (1), the first and second reversive counters (2, 3). ^ EFFECT: simplified hardware implementation of digital filter for assessment of slowly changing median of signal. ^ 1 dwg, 1 tbl

Description

The invention relates to specialized means of computer technology and can be used in systems that require hardware-based implementation of digital signal filtering algorithms, for example, when estimating a zero level against a background of pulsed signals / interference or in conditions of a dynamic range limitation asymmetric with respect to a zero level.

Known digital median filter [1], consisting of nodes for counting the number of samples, nodes for ordering numbers, comparator, control unit and clock.

The well-known median filter has the disadvantages characteristic of the hardware implementation of median filtering: high resource consumption and circuit complexity.

The closest technical solution to the proposed digital filter circuit is a device [2], including an analog-to-digital converter, a generator, a digital comparator, a reversible counter, the first and second elements I.

A disadvantage of the known digital filter is that its algorithm implements an estimate of the average value, and not the median of the signal, therefore this device cannot be used to estimate the zero level in the above conditions.

The objective of the invention is the development of a schematically simple (in comparison with traditional median filters) hardware implementation of a digital filter for evaluating a slowly changing median of a signal.

This is achieved by the fact that in the digital filter for evaluating the slowly varying median of the signal, containing a digital comparator and a first reversible counter, a second reversible counter is additionally introduced, the first clock signal being connected to the clock input of the first reversing counter and the second clock signal connected to the clock input the second reverse counter and with the preset input of the first reverse counter, the input bus is connected to the first code input of the digital comparator, the output bus the signal is connected to the code output of the second reversible counter and the second code input of the digital comparator, the output of the digital comparator and the senior (signed) bit of the first reversible counter are connected to the input direction control of the counting of the first and second reversible counter, respectively.

- первый тактовый сигнал, соответствующий частоте дискретизации, f

/N - второй тактовый сигнал, соответствующий частоте дискретизации, деленной на N=2^m(m=1, 2, 3…).The drawing shows a block diagram of the proposed digital filter for evaluating the median of the signal, where 1 is a digital comparator, 2 and 3 are the first and second reversible counters; x, y - input and output signal buses, respectively, f

- the first clock signal corresponding to the sampling frequency, f

/ N is the second clock signal corresponding to the sampling frequency divided by N = 2 ^m (m = 1, 2, 3 ...).

The proposed digital filter circuit implements the following algorithm for estimating the median signal:

. Анализ данного выражения показывает, что оценка медианы с помощью алгоритма, корректирующего предыдущее значение оценки так, чтобы в каждой выборке длины N количество отсчетов больших и меньших либо равных текущему значению оценки были равны, т.е. с помощью алгоритма (1), является состоятельной.where x _i are samples of the amplitude of the input signal, [i / N] is the integer part of i / N. From the definition of the median as a 0.5th-order quantile, it follows that

. An analysis of this expression shows that the median is estimated using an algorithm that corrects the previous value of the estimate so that in each sample of length N the number of samples greater than or less than or equal to the current value of the estimate is equal, i.e. using algorithm (1), is consistent.

, и оценки медианы, полученной по предыдущим N отсчетам. При этом результат сравнения берется со знаком плюс, если x_i больше либо равно текущей оценке медианы, и со знаком минус в противном случае. В зависимости от знака числа, получаемого в первом реверсивном счетчике 2 после N операций сравнения и накопления (старший разряд первого реверсивного счетчика 2), значение второго реверсивного счетчика 3 либо увеличивается, либо уменьшается на единицу младшего разряда раз в N тактов. Разрядность второго реверсивного счетчика 3 равна разрядности отсчетов входного сигнала.The first reversible counter 2 has a capacity of m + 1 and generates a signal s _{i, j} , i.e. calculates the sum of the results of comparisons of samples x _i received with a frequency f

, and estimates of the median obtained from the previous N samples. In this case, the comparison result is taken with a plus sign if x _{i is} greater than or equal to the current median estimate, and with a minus sign otherwise. Depending on the sign of the number obtained in the first reversible counter 2 after N comparison and accumulation operations (the highest digit of the first reversible counter 2), the value of the second reversible counter 3 either increases or decreases by a unit of the least significant digit every N cycles. The resolution of the second reversible counter 3 is equal to the resolution of the samples of the input signal.

According to the results of modeling normal white noise filtering, an approximation of the numerical dependence of the standard deviation at the filter output on the standard deviation at the input and the sample length N is obtained:

,

,

where k≈0.9. Normalized mean square error of approximation (standard deviation / 2 ⁿ ,

where n is the bit depth of the signal samples) does not exceed 10 ^-3 .

We estimate the minimum equivalent noise reduction coefficient

.

.

таким, чтобы 99% отсчетов входного сигнала укладывались в динамический диапазон, для нормального шума имеем

, т.е.

. На практике удобно пользоваться соотношением

. Коэффициент подавления шума традиционного медианного фильтра равен

. Видно, что алгоритм (1) подавляет шум во входном сигнале на несколько порядков сильнее, чем медианный фильтр.To do this, select the value

so that 99% of the samples of the input signal fit into the dynamic range, for normal noise we have

, i.e.

. In practice, it is convenient to use the relation

. The noise reduction coefficient of a traditional median filter is

. It can be seen that algorithm (1) suppresses noise in the input signal several orders of magnitude stronger than the median filter.

Table Comparative data on hardware costs Filter type Aperture Length (Samples) Number of configurable logic blocks Median 5 31 7 49 9 60 Estimation using algorithm (1) 8 3 64 four 256 four

The proposed digital filter scheme provides a significant reduction in hardware costs compared to the traditional median filter, where many schemes for comparing and arranging samples are required. The table shows comparative data on the hardware costs for implementing the estimation algorithm under consideration and the median filter for processing 8-bit samples based on the Xilinx Spartan 3 FPGAs.

Thus, the developed digital filter scheme for evaluating a slowly changing median has the following features:

- simplicity of circuitry implementation;

- significant saving of system resources;

- several orders of magnitude greater normal noise rejection compared to traditional median filters.

Information sources

1. Institute for Analytical Instrumentation RAS. Digital median filter. Description of the invention to the patent of the Russian Federation No. 2043654, G06F 17/18, 09/10/95.

2. JSC "Rocket and Space Corporation" Energy "them. S.P. Korolev. " A method for digitally filtering signals and a digital filter for implementing this method. Description of the invention to the patent of the Russian Federation No. 2188499, 7 H03H 17/02, 04/07/2000.

3. Huang T.S. Fast algorithms in digital image processing. - M .: Radio and communications, 1984. - 224 p.

Claims (1)

A digital filter for estimating a slowly varying median of a signal, comprising a digital comparator and a first reversible counter, characterized in that a second reversible counter is introduced into it, wherein the first clock signal is connected to the clock input of the first reverser counter and the second clock signal is connected to the clock input of the second reverse counter and with the input of the preset of the first reverse counter, the input signal bus is connected to the first code input of the digital comparator, the output signal bus is the code key to the output of the second up-down counter and a second code input of a digital comparator, the output of the digital comparator and Senior (sign) bit of the first up-down counter connected to the counting direction control input of the first and second up-down counter respectively.