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The instantaneous frequency of a sine wave can be estimated using a Hilbert transformer. However, there is a ripple in the amplitude characteristics of finite-order Hilbert transformers. The estimate thus contains an oscillatory component that depends on this ripple. In this paper, we theoretically show that the frequency of the oscillation component is an even multiple of the input signal frequency. We propose a method for designing a low-pass FIR filter with variable transmission zeros. A simulation is used to show that this filter improves estimation accuracy.

Frequency estimation is used in a wide range of areas such as radar, telecommunications, voice analysis and weight measurement using tuning fork sensor. This paper describes an instantaneous frequency (IF) estimation method. The original signal combined with the Hilbert transform form a complex analytic signal. The phase of the analytic signal is defined as the instantaneous phase and the time derivative of its phase IF. However, the amplitude of the signal obtained by phase-shifting the input signal by 90 degrees is different from that of the input signal because a ripple is generated in the frequency characteristics of the finite-order finite impulse response (FIR) Hilbert transformer (HT). As a result, errors are contained in the IF. In this paper, we propose a highly accurate IF estimation method using a notch filter. It is shown analytically that a harmonic frequency component is included in the IF obtained by using a finite-order FIR HT. Then, it is shown that the accurate instantaneous frequency can be obtained by removing the harmonic frequency component using an infinite impulse response (IIR) notch filter. Finally, the effectiveness of the proposed method is shown in simulations.

To measure mass of goods, automatic checkweighers are widely used, and is composed by a sensor of scale and a conveyor-belt. Variable digital filters (VDFs) are used to reduce the noise overlapping on the measurement signals in the instruments. The VDFs have piecewise high attenuation in the stopband to reduce delay. Conventional VDFs were difficult to obtain the desired piecewise high attenuation in order to change the attenuation by weight function. In this paper, we are proposed a design method for equiripple linear-phase FIR filters having multiple variable components in the stopband and the specified piecewise high attenuation. The proposed method adds a constraint in the minimax design problem, that directly changes piecewise high attenuation band by a variable parameter. The optimization methodology known as semi-definite programming (SDP) is used. The obtained VDF has high attenuation in part of the stopband, and then its attenuation, position, and stopband edge frequency are variable. Effectiveness of the proposed method is illustrated by a design example.

In general, a design of digital filters is used computers having relatively long bit length. On the other hand, filter coefficients could be rounded to the specified number of bit length, when digital filters are implemented embedded equipment. Then, filter characteristics may become degradation. It is difficult to realize high accuracy measurement. In this paper, we propose a finite bit length design method of variable digital filters with variable multiple elements of stopband. Proposed variable filter's coefficients are approximated by polynomial using variable parameters, and the polynomial coefficients are composed by finite bit length. The design problem is multiple objective optimization due to variable multiple elements. Then, we propose individual evaluation method for design variable digital filters using a genetic algorithm. Finally, effectiveness of the proposed method is shown by a design example.

Two-dimensional (2-D) linear phase maximally flat finite impulse response (FIR) digital filters have flat passbands and stopbands. Conventionally, there are only fan-shaped or diamond-shaped. In this paper, we propose a method for designing 2-D low-pass maximally flat FIR digital filters that can realize various passband shapes. The proposed transfer function is achieved as a closed-form expression, and various passband shapes can be created by changing the filter order or flatness degree.

This paper describes a general expression of the transfer function of the low-pass maximally flat FIR digital differentiator (low-pass MFDD). The low-pass MFDD provides extremely high accurate differentiation around ω = 0. Simultaneously, it can reduce noises in the high frequency. However, the conventional design method of the low-pass MFDD is designed with the linear phase characteristics. By contrast, the proposed method can adjust the value of the group delay at ω = 0, so that the proposed method can realize not only the linear phase characteristics but the low or the high delay characteristics.

In this paper, we propose a design method for complex coefficients FIR variable digital filter (VDF) with changeable multicomponent in the stopband. The proposed VDF has piecewise high attenuation in the stopband, and the VDF varies some characteristics in the stopband using variable parameters. The complex filter coefficients are composed polynomial expression using variable parameters to vary the filter characteristics. The proposed method, the minimization problem for the complex coefficients FIR VDF with changeable multicomponent are formulated as semidefinite programming (SDP) in the frequency domain. Finally, we demonstrate the effectiveness of the proposed method.

Finite impulse response (FIR) transmitter and receiver filters for data transmission require both frequency domain and time domain approximation simultaneously. Previously, linear programming techniques have been used to design such filters; however, those techniques require many calculations and lengthy computation time. Proposed here is the design method of FIR transmitter and receiver filters for data transmission that uses the successive projections method. The design method of a matched filter pair is first described. It can have maximum signal-to-noise ratio (SNR) when Gaussian noise exists on the transmission line and where both the transmitter and receiver filters have the same amplitude response. Since the matched filter has double zeros in the stopband, it can also be used to derive the transfer function of a bandpass minimum phase filter. Then, the value of zero in the sampling interval is chosen such that total impulse response of the matched filter pair has zero intersymbol interference. A design method with constraint in time domain is thus described.

A applicability of Successive Projections (SP) method is wide. In the previous SP method which is an iterative approximation method, only one extreme frequency point at which the deviation from the given specification is maximized is used in the update of the filter coefficients. We extended to SP method which can update the filter coefficients by the multiple extreme frequency points using Fritz John's theorem. In this method, the solution is obtained less iteration number than the previous method. However, because it is necessary to decide the maximum allowable error experientially, there is the case that the solution does not converge and the obtained filter does not have equiripple characteristics. In this paper, we present a design method of linear phase FIR filters by SP method updating maximum allowable error. The updating maximum allowable error analytically solves such as Remez algorithm. Finally, we confirm the effectiveness of propose method through several examples.

In this paper, we propose a design method for finite impulse response (FIR) variable digital filters (VDFs) obtaining quasi-equiripple characteristic even if notch frequencies change. The change in filter coefficients, which depends on the change in notch frequencies, is approximated by a polynomial using variable parameters. In this method, the minimization problem for the polynomial coefficients with variable notches is formulated as semidefinite programming (SDP) in the frequency domain. However, the number of polynomial coefficients increases when variable parameters are plural number. Therefore, we also propose a method for reducing the number of polynomial coefficients. The usefulness of the proposed VDF is demonstrated through examples.

In the field of measurement signal processing, we should often change the characteristic of the stopband instantaneously. Such the filter that can change the frequency response instantaneously is called variable filter. We propose the design of FIR digital filters with variable stopbands. In this paper, the quasi-chebyshev characteristic is obtained by using an iterative weighted least square (WLS) method. Moreover, a memory required for the calculation for computing filter coefficients in the proposed method has the feature of being fewer than the conventional method. The usefulness of the proposed design method is verified through some examples.

In this paper, we propose a transfer function of filters which does not change filter characteristics even if notch frequency changes. A change in filter coefficient which depends on change in a notch frequency is approximated by the polynomial which used a variable parameter. In this method, the minimization problems for the coefficients of the filter with a variable notch are formulated as semidefinite programming (SDP) in the frequency domain. Moreover we present that the proposed VDF can be implemented using the Farrow structure suitable for high-speed signal processing.

In this paper, we define filters capable of changing frequency response characteristics as variable filters. Digital filters capable of changing their frequency response are such as group delay, magnitude response and resonance frequency, etc.. In this paper, we propose a design method for FIR digital filters with an arbitrary variable fractional delay by convex projections algorithm. Then each coefficients of variable filter represents as different polynomials of M order using a set of spectral parameters. Finally, the usefulness of the proposed method is verified through the examples.

Several applications in digital signal processing demand variable digital filters with arbitrary variable frequency response. However, the design method of filters having variable piecewise large attenuation characteristics in the stopband is not proposed. This paper describes the design method of variable FIR digital filters having changed piecewise large attenuation characteristics in the stopband. The basic idea is to represent the coefficients of variable transfer function as the polynomials using spectral parameter. We design each filter with difference stopband attenuation by successive projections method. Then we approximate the obtained filter coefficient by the polynomials using spectral parameter in the least-square sense.

This paper presents a directly design method of FIR filters with minimum phase characteristics using successive projections (SP) method. We use Rouche's theorem for coefficients update algorithm in SP method to restrict the roots of transfer function inside the unit circle and on the unit circle. The proposed method is an iterative optimization technique and its algorithm is as simple as the conventional SP method. The usefulness of the proposed method is verified through the examples.