Designing linear phase FIR digital filters with flat passband and equiripple stopband characteristics

Abstract

SUMMARYIt 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.

Perfect linear phase IIR filter with flat passband amplitude and equiripple stopband attenuation characteristics

“…In addition, the frequency components near the band edges often carry detailed information on the waveform even though their energies are small. Therefore, filters with extremely flat amplitude characteristics at DC or near the center frequency and flat amplitude in the entire passband, or a few small-amplitude ripples only near the band edges, are superior to filters with equalripple amplitude characteristics in the entire passband in the sense that the waveform distortion caused by the filter is smaller [10][11][12][13]. Also, although Zhang and Iwakura presented design examples of real-coefficient low-pass filters, no examples have been presented of a real-coefficient bandpass filter [5].…”

“…Since an FIR filter can realize a perfect linear phase characteristic, this filter is useful if the required cutoff characteristic is moderate so that only a low order is needed. However, if a sharp cutoff characteristic is required, the order becomes high and the amount of computation increases [10][11][12][13]. In this case, a linear phase IIR filter is suitable because of the small amount of computation required [9].…”

An Analytical Approach for Design of Nth-band FIR Digital Filters with Equi-Ripple Passband

“…FIR filters are used widely because they have a characteristic of linear-phase, which IIR (Infinite Impulse Responses) filters do not have [1] [2]. In addition, FIR filters are necessary in constructing optimal interpolation and decimation filters with a characteristic of linearphase during over-sampling and down-sampling process in multi-rate digital systems [3] [4].…”

Design of Low Delay Bandpass Fir Filters With Maximally Flat Characteristics in the Passband and the Transmission Zeros in the Stopband

“…Accordingly, to reduce echoes and ringing and to maximize the stopband attenuation, it is important to design FIR filters with maximally flat characteristics in the passband and transmission zeros in the stopband. The design method of such FIR filters by Remez algorithm has been proposed (Selesnick and Burrus, 1996;Aikawa and Sato, 2000). However, since the delay of linear-phase filters is half of filter length, the delay of linear-phase filters will become large when high-order filters are required.…”