Improved Two-Stage Decimator Structure Using Kaiser Hamming Sharpening
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Improved Two-Stage Decimator Structure Using Kaiser Hamming Sharpening Supriya Aggarwal1 Received: 16 January 2020 / Revised: 29 October 2020 / Accepted: 4 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose an efficient two-stage decimator structure based on Kaiser Hamming sharpening (KHS) of moving average filter. The proposed KHS decimator divides the overall decimation factor M = M1 M2 , such that both M1 , M2 ∈ Z+ . The first stage uses KHS with first and second order of tangency at unity and zero, respectively. The second stage uses the simplest KHS sharpening, i.e. first-order tangency at both unity and zero. The architecture of the proposed structure is designed to match the existing decimator to have nearly equal number of integrator sections operating at high sampling frequency of f s . The pass-band droop at the normalized pass-band cut-off frequency of 1/2M in the proposed design is 13.8% less as compared to the existing KHS decimator, with a compromise of 3% in alias rejection. Further, as the normalized pass-band cut-off frequency is reduced to 1/4M, the proposed design in comparison to existing decimator has 34.5% less droop with only 2.3% compromise in alias rejection. Keywords FIR filters · Moving average filter · Kaiser Hamming sharpening · Decimation
1 Introduction In the domain of digital signal processing, design of efficient multi-rate systems is an active research area [13–15] where signals with different sampling frequencies are processed simultaneously. Decimation filter is one such filter which scales the original sampling frequency by a factor 1/M; thereby reducing the original Nyquist frequency from f s /2 to f s /2M. The simplest way to realize a decimation filter is to use a recursive running sum (RRS) filter [15], also referred to as the moving average
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Supriya Aggarwal [email protected] Department of Electronics and Communication Engineering, MANIT, Bhopal, India
Circuits, Systems, and Signal Processing 0
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Fig. 1 Frequency response of the MA filter with M = 8 0 Alias Frequency Bands
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Fig. 2 Frequency response of MA filter as a decimator with M = 8
(MA) filter, given by: 1 H (z) = M
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where M defines the length of the MA filter and also the decimation factor if used as a decimator. The frequency response of the MA filter has nulls centred around the normalized frequency 2 p/M, where p ∈ Z+ , as shown in Fig. 1. Using the MA filter as a decimator needs consideration as the desired pass-band cut-off (given by frequency f p ) is replicated around these nulls as shown in Fig. 2. This requires that the magnitude in pass-band [0, f p ] is constant and the closest alias frequency (2/M − f p ) is
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