Decimation filters with minimum number of additions per output sample

Abstract

In multistage decimation filters some stages operate at the low sampling rate, thus reducing the required number of additions per output sample (APOS). State-of-the-art methods for the design of these filters usually consider only two stages. In addition, these methods do not optimize the number of APOS explicitly. This Letter proposes a framework for the design of multistage decimation filters with minimum number of APOS. To accomplish this task, the structures which contain maximum number of stages allowed by specified decimation factor are optimized. As a case study, multistage filters whose stages are cascaded-integrator-comb filters are considered. It is illustrated by several examples that the proposed optimum filters ensure smaller number of APOS and higher folding-band attenuation than those obtained by recent methods for multistage filter design.

Design of Decimation Filter With Improved Magnitude Characteristic and Low Complexity

“…The design of a multistage decimation filter with a minimum number of APOS for a given decimation factor and minimum worst-case attenuation was proposed in [10]. For comparison, we take an example for M=15, as given in Table 4 in [10].…”

“…The design of a multistage decimation filter with a minimum number of APOS for a given decimation factor and minimum worst-case attenuation was proposed in [10]. For comparison, we take an example for M=15, as given in Table 4 in [10]. The distribution of integrators and combs along the stages are L k =-4,-5,9; the decimation factors are R m =5,3.…”

“…The distribution of integrators and combs along the stages are L k =-4,-5,9; the decimation factors are R m =5,3. The minimum attenuation is δ [10] =81.4dB, and the total number of APOS NC [10] =84. In the proposed method, the design parameters were M 1 =5, M 2 =3, K 1 =K 2 =4.…”

“…It can be observed that the proposed filter has less APOS. The compensator from [8] was applied in [10] with the reported coefficients: [511, -240, 72, -12] requiring 10 adders and resulting in maximum deviation of δ [10] =0.053dB. It is worth mentioning that this compensator, unlike the proposed compensator, does not force compensators-unity gain and should be normalized.…”

“…The methods for the simultaneous improving the comb passband and stopband, based on sharpening technique, are proposed in [7]- [9]. Recently, in [10] is presented method for design of decimator with a minimum complexity expressed in the number of adders per output sample.…”