UA12439U - Method for synthesizing a digital filter - Google Patents

Abstract

The present invention relates to a method for synthesizing a digital filter that can be used in radio transmitting and receiving devices, communication systems, and correcting devices of automatic control systems. The proposed method is based on the presentation of the filter response by an operational fractional rational transfer function of order n: The method is distinctive by using operations that are performed by three units designed for the realization of the method. The first unit provides the calculation of the minor derivatives of the output signal of the filter, so that each derivative is determined as the sum of its preceding value and the product of the sampling interval by the current value of the next order derivative. The second unit is designed for calculating the higher derivative of the output signal of the filter, so that the derivative value is determined as the sum of the input signal of the filter and the inverse values of the paired products of all the minor derivatives and the coefficients of the system characteristic operator with indices that are equal to the order of the derivative being multiplied. The third unit is designed for generating the output signal of the filter as the sum of all the calculated derivatives multiplied by the coefficients of the characteristic operator with indices that correspond to the order of the derivative being multiplied. The proposed method is distinctive by its versatility, which provides a possibility to synthesize digital filters with arbitrary coefficients of the transfer function of the filter. The procedure for determining, in the second unit, the higher derivative of the output signal of the filter as the sum of the input signal of the filter and the inverse values of the paired products of all the minorderivatives and the coefficients of the system characteristic operator with indices that are equal to the order of the derivative being multiplied is used as a feedback procedure that provides a possibility to increase the accuracy and stability of the filter.

Description

Description of the invention

The useful model refers to radio engineering, in particular, the synthesis of signal filtering devices and can be used in automation and telemechanics when solving control system correction problems.

A known method of filter synthesis (1) is based on discrete signal transformation. Its disadvantage is the complexity of implementation.

As a prototype, the method chosen according to the a.s. Mo1828551, IPC 50585/01 | Nonlinear filter, BI Mo26, 1993, p. 124). Its disadvantage is limited functionality. 70 The useful model is based on the task of implementing a filter based on a given normalized fractional-rational transfer function of the form:

MV) KRUSHr) where ti o is the operator of the action, p o is the own operator, /P is the order of the action operator, 7 is the order of the tr)- Vr skrivar i-0 and i-th own operator, tep, ad-1, on based on the description of the filter response in the recurrent form, we - sweat p "ya. dr kt ХК zate (2 t .

Tk U Kk (3 yin where Uk is the output signal, chi is the youngest |-th derivative of the output signal, cha is the oldest p-th derivative of the output signal, ху is the input signal, НЯ is the sampling step, К is the step number.

In the description of the filter response, the coefficients of the action operator and the eigenoperator can take arbitrary values, which ensures the universality of the proposed method, which allows synthesizing filters of arbitrary configuration, subject to the specified implementation conditions (tep and ad-1).

Thus, the proposed filter synthesis method allows you to solve the problem in a wide range of possible parameters. co

The essence of the proposed useful model is expressed by a set of the following significant features: the output signal of the digital filter is formed by the sum of even products of the derivatives of the output signal of the filter and the coefficients M of the action operator with indices coinciding with the order of the derivatives that are multiplied. The older derivative of the output signal of the filter is the summation of the input signal of the filter with the inverse values of the even products of all the younger derivatives and the coefficients of the eigenoperator, the indices of which coincide with the order of the derivatives being multiplied. Each younger derivative is obtained recursively by summing its previous value, which is fixed by the memory element, with the product of the discretization step by the current value of the older derivative by one order. "

Figure 1 shows a diagram explaining the essence of the proposed useful model. It consists of three - 70 sub-blocks with numbers 1, 2 and 3, implementing dependency (1), (2) and (3), respectively. Subblock 1 is designed to find the lower derivatives of the output signal by performing for each of them operations of multiplication with" (Rhod) of the current value of the older derivative by one order per discretization step, adding (5!yt) the result of multiplication with the previous value of the determined derivative, registered element memory (Met). The obtained values of the lower derivatives of the output signal are fed into sub-block 2 to determine the higher derivative U from the 45 values of the lower derivatives of the filter output signal found in sub-block 1. For this purpose, each derivative is multiplied by the coefficient a; (1-0...n) of the own operator with an index equal to the order of the derivative, and is fed to the inverse input of the adder (Zyt II adder), to the direct input of which the input signal of the filter x is connected. As a result of this, the higher derivative M "7 is formed at the output of sub-block 2. The resulting derivatives are fed to the input of sub-block Z, where they are multiplied by the coefficients Бо, бу, ..., Б, "2. Bt of the action operator with indices equal to the order ( 95) 50 derivatives that are multiplied. The resulting even products are summed (adder Z!it I), forming the output signal of the filter U. In Fig. 1, the index of the step number K is omitted in the notation of the signals.

The proposed method is universal, allowing synthesis of filters with arbitrary values of the coefficients of its transfer function. The introduction of the procedure for calculating the senior derivative M "corrects the process, increasing the stability and accuracy of the digital filter.

Bibliographic list: p. 1. Adaptive filter!: Trans. with English / Ed. K.F.N. Kouzna and P.M. Granta, - M.: Mir.

Claims (1)

The formula of the invention The method of synthesizing a digital filter is based on modeling the response of a filter with a normalized operator fractional-rational transfer function of the form: Ти НШ . 1 in povo /Ссвы и-о и-и which differs in that the output signal of the filter is obtained by summing the even products of the coefficients of the action operator with indices corresponding to the order of the derivatives of the output signal of the filter on these derivatives, the value of which is the summation of the result of multiplying the current value of the older by one order of the derivative per sampling step with the previous value of the resulting derivative registered by the memory element, and the older derivative of the filter output signal is the summation of the filter input signal with the inverse values of the paired products of all the younger derivatives of the filter output signal and the coefficients of the eigenoperator whose indices coincide with the order derivative that is multiplied. that 2 (o) (ze) « s yo - and? - name) sh" (95) 3e) 60 b5