Kotaro Hirano

Design of digital notch filters

It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

Mean-squared error analysis of an adaptive notch filter

A mean-square-error analysis of the steady-state coefficient fluctuation of an infinite impulse response (IIR) adaptive notch filter, whose coefficients are estimated by simple gradient and sign gradient algorithms, is presented. Regarding the magnitude and phase responses of the transfer function that is used to realize a second-order IIR adaptive notch filter, it is shown that the filter-coefficient estimation error can be studied by using first-order ordinary difference equations with stochastic input. Simple closed-form results are derived for the mean-square error of the steady-state coefficients. The results of computer experiments are presented to substantiate the analysis.<<ETX>>

Design of Digital Notch Filters

It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

A new class of very low sensitivity and low roundoff noise recursive digital filter structures

A class of new structures is proposed, for the realization of the recursive digital filter with poles near the unit circle, by introducing the particular type of delay replacement scheme in the existing digital filter structure and then, inserting, delays at the. proper places to avoid the delay-free loops. By applying the proposed method to the second-order direct form structures, new structures are found with very low magnitude transfer function sensitivities with respect to multiplier coefficients and low roundoff noises. Some numerical results are also presented.

Design of Digital Sinusoidal Oscillators with Absolute Periodicity

The design of digital sinusoidal oscillators with finite word lengths having excellent periodicity is proposed. The design utilizes the fundamental properties of a simple second-order difference equation containing a single multiplication coefficient. Two different design methods are outlined. In the first method, a set of values of the multiplier coefficient and the initial states are selected appropriately to guarantee periodicity after quantization. In the second method, periodicity is insured by forcing one or two selected future sample values equal to certain past sample values. Experimental results of the hardware implementation of oscillators designed using both methods are included.

Active RC filters containing periodically operated switches

The state-variable approach to inductorless filters that utilize resistors, capacitors, gyrators, controlled sources or negativeimpedance converters (NIC), and switches suitable for integration is described. By using the state equations of active RC networks in the standard form, it is shown that multiplications of resistances, gyration conductances, transfer coefficients of controlled sources, and NIC in active RC network can be achieved by means of the switching technique. From these results, the relations between the input and the output at signal frequency of active RC filters containing periodically operated switches are derived at the steady state for the case where the switching frequency is much higher than the signal frequency. The results show that the cutoff and the center frequencies of active RC filters are adjustable by changing the ratio of the on duration in a period to the period of switching. The experimental results of low-pass, bandpass, and high-pass filters are shown along with the theoretical curves.

Design of digital bandpass/bandstop filters with independent tuning characteristics

Two different approaches are proposed in this paper for the design of bandpass/bandstop filters with independent tunning of the center (notch) angular frequency ω 0 and the 3-dB attenuation (notch) bandwith Ω c . These approaches lead to a variety of two-multiplier structures for the realization of second-order bandpass/bandstop digital filters in which one multiplier controls ω 0 and the other multiplier adjusts Ω c

Explicit design formulae for digital tan filters with low-pass, high-pass, band-pass, and band- stop characteristics

Abstract Explicit expressions of transfer functions for digital tan filters with low-pass, high-pass, band-pass, and band-stop characteristics approximating given design specifications are advanced. The higher order transfer function satisfying the design specification is expressed as the product of first-order and second-order filter sections of identical forms but with different coefficient values. All coefficients of these low-order filter sections are expressed in explicit forms related simply to the specification values. Thus, the result developed can be easily applied for the cascade or time-sharing realization. The low-order filter section developed here can be implemented with the fewest multipliers. The design formulae for Butterworth, Chebyshev, inverse Chebyshev and elliptic approximations are included. The transfer functions for all these filters are expressed in the same form of low-order filter section with different coefficient values.

Theory and applications of all-digital N-path filters

The all-digital N -path filter structure for the processing of discrete-time signals is introduced. The structure is made of N parallel paths having identical time-invariant digital filters. The filters are connected to a common input signal path through input modulators, and a common output signal path through output modulators. The modulators produce identical periodic sequences but are staggered in phase from filter to filter. A detailed time-domain and frequency-domain analysis of the N -path filter is provided. It is shown that for certain bandlimited modulating sequences, or by appropriately bandlimiting the input and output signals, the overall time-varying structure can be made to appear as a timeinvariant network. This approach leads to filters with adjustable characteristics, and it is shown that by time-sharing the time-invariant digital filter path N times, it is possible to design filters with complex characteristics quite economically. A number of useful modulating functions are described, and some possible applications are discussed.

N-path digital filters

According to the sampling theorem, a faster sampling rate is required in order to process signals containing high frequency components. The processing rate is restricted by the highest operating speed of devices available. This paper presents the design of N-path parallel processing technique which would overcome the speed limitation of present devices. The transfer function of N-path digital filter is shown to be H(zN), where H(z) is the transfer function of each component filter block. This implies that the overall magnitude response of N-path digital filter is a frequency scaled version of that of component filter. In the proposed paper, a scheme to cancel out the unwanted passbands by cascading several N-path filters is first discussed. Then the design procedure of N-path filter from given specification is illustrated using simple example.