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In the field of digital signal processing, there are cases in which the frequency characteristics must be changed instantaneously in response to the processing objective. A filter whose characteristic can be varied instantaneously is called a variable filter. Many reports are available on the design of FIR digital filters with a variable passband. However, it appears that there are no publications on the design of an FIR digital filter in which the portion of the stopband with high attenuation can be varied. In this paper, a design method is proposed for an FIR digital filter using spectral parameters that make the portion of the stopband with high attenuation variable. For the design, the successive projection method with a simple algorithm is applied. A filter with an almost equal-ripple profile for the entire amplitude characteristic is designed by varying the spectral parameters. As a result, it is possible to obtain amplitude characteristics close to those of the filter solved by the Remez algorithm for specifications that change instantaneously from time to time. Finally, a design example is presented to confirm the effectiveness of the present approach. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(4): 34–41, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20176

It is known that linear phase FIR digital filters fall into four types considering the symmetry of impulse response. For example, filters of type 2 can be used at the time of partitioning and reconstruction of signals in multirate signal processing, and other types have similar special applications. Moreover, the linear phase FIR digital filters with flat passband and equiripple stopband characteristics are very important filters in practice because they have better time domain characteristics and less ringing than Chebyshev filters with equiripple stopband and passband characteristics. However, conventional design methods are restricted to type 1. In this paper, we therefore propose a method of design of linear phase FIR digital filters with flat passband and equiripple stopband characteristics for all four types. The proposed function is composed of two functions, one with a flat characteristic in the passband and the second with equiripple characteristics in the stopband. The latter function is obtained by using the well-known Remez algorithm only for the stopband. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(4): 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1148

In analog filters with monotonic amplitude characteristics, there exists a significant difference in the flatness between Butterworth filters and L filters. However, there are no reports on low-pass analog filters with characteristics that are intermediate of those two, that is, in which the amplitude is monotonic and the flatness is arbitrary. In this paper, by means of Jacobi polynomials, a mathematically closed transfer function of such a filter is proposed. The proposed transfer function incorporates those of Butterworth filters and L filters. Also, this transfer function can be realized at arbitrary order for both even and odd orders. © 1999 Scripta Technica, ElectronComm Jpn Pt 3, 82(8): 21–29, 1999

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.

The cascade of a prefilter and an equalizer is effective for realizing an FIR digital filter with few multipliers. Generally, the number of multipliers in the entire filter decreases as the prefilter response becomes closer to a given specification. This paper proposes a new structure of pre-filters which can produce a response closer to the specification than a conventional structure. Furthermore, a new method of cascading the prefilters, and which improves both the passband and stopband characteristics, is described. In this method, a pre-filter cascaded with the preceding ones is designed so as to compensate their approximate characteristics. the small passband ripple and large stopband attenuation can be realized by using the proposed prefilters and an equalizer with only few multipliers.