S.C. Dutta Roy

Design of digital differentiators for low frequencies

Optimal, maximally accurate digital differentiators (DDS) are derived for the low-frequency range. Exact coefficients used in the proposed DDs can be readily computed from explicit formulas, whereas the optimal (minimas RE) DDs require and optimization program to derive the coefficients. The lower the frequency of differentiation, the better is the performance of the proposed differentiators, making them suitable for many typical applications. >

Maximally linear FIR digital differentiators for high frequencies

The frequency response of conventional FIR digital differentiators (DD), using only integral delays, is poor towards the high frequency end, and becomes identically zero at w= pi . To overcome this problem, a half-sample delay, z/sup -1/2/, is used in the minimax relative error DDs. However, the order of such DDs grows exponentially when accuracies better than 99.0% are desired. The authors propose maximally linear DDs, using one half-sample delay, which can achieve a frequency response accuracy better than 99.9%, with attractively low orders for 0.5 pi >

RC active all-pass networks using a differential-input operational amplifier

This letter contains a generalization of some recently published RC active all-pass networks using a differential-input operational amplifier and presents a synthesis procedure for all-pass transfer functions of any arbitrary order, having poles confined to the negative real axis. Examples are given to illustrate the synthesis procedure.

Design of efficient second and higher order FIR digital differentiators for low frequencies

Digital differentiators of orders greater than unity are often required in processing various types of data in a number of practical applications. In many of these, the vital information in the signal is contained in the low frequency range. We propose, in this paper, a new and efficient design of FIR digital differentiators of second and higher orders for the low frequency range. Mathematical relations have been established between the weighting coefficients of the maximally linear (first order) FIR digital differentiators and those of the proposed (second and higher order) differentiators. Recursive as well as explicit formulas for the weighting coefficients of the second order differentiators have also been derived. Extremely high accuracies are obtainable from the proposed differentiators, for attractively low orders of the filters.

A circuit for floating inductance simulation

An active RC realization of a lossy floating inductor is presented. The circuit uses two operational amplifiers--each in the unity gain connection--three resistors, and two capacitors, and has low L and Q sensitivities to passive as well as active components.

Linear phase variable digital bandpass filters

A transformation for obtaining a linear phase variable cut-off low-pass digital filter has been recently described in the literature [1]. In this letter, this transformation is worked out for the case of linear phase bandpass digital filters with variable bandwidth and center frequency.

Explicit formula for the coefficients of maximally flat nonrecursive digital filter transfer functions expressed in powers of cos w

An explicit formula for the coefficients of the transfer function of a maximally flat nonrecursive digital filter, expressed in powers of cos w, is derived by exploiting the properties of the Kaiser-Hamming [1] amplitude change function polynomial. Transfer functions expressed in this form are convenient for implementing variable cutoff filters [2].

Active all-pass filter using a differential-input operational amplifier

Horowitzs active RC synthesis procedure with a voltage controlled current source is combined with Sheingolds realization of the active element using a differential-input operational amplifier to derive a circuit for an all-pass filter of any arbitrary order, having poles confined to the negative real axis only. Illustrative examples are worked out for the first- and second-order cases.

Design of IIR digital notch filters

A method is presented for the design of notch filters with specified notch frequency Ω0 and 3-dB rejection bandwidthBt, using a first-order real all-pass filter, wherein the only coefficient is used to control the notch frequency. To control the bandwidth, use is made of a new amplitude change function (ACF), and it is shown that given notch filter specifications can be exactly met thereby. Also, using the ACF, it is shown that stability of the second-order notch filter designs can be improved along with the noise gain.

On the design of efficient second and higher degree FIR digital differentiators at the frequency p/(any integer)

In a number of signal processing applications, digital differentiators (DD) of degree greater than unity performing over a narrow band of frequencies are required. The minimax relative error DDs are especially suitable for broad band applications, but they become inefficient when adopted for narrow band situations. This paper proposes second and higher degree DDs which are maximally accurate at the spot frequency: π/(any integer). Mathematical relations have been established between the weighting coefficients of the first degree FIR digital differentiators which are maximally linear at the frequency π/(any integer) and those of the proposed (second and higher degree) differentiators. It has been shown that very high accuracies in the frequency response of the approximation are achievable with attractively low order of the structure for the suggested differentiators. As an example, with just 16 multiplications per input sample of the signal, it is possible to obtain a third degree differentiator over a frequency bandwidth of 0.20π centred around ω = π/3, with an accuracy no worse than 99.999%. The phase error is zero over the entire frequency band 0⩽ω⩽π of operation.