Sinc Sum Function and Its Application on FIR Filter Design

Wang, Yunlong

doi:10.1007/s10440-009-9492-7

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…(ii) let K=2, select 3 points v=0, v=2.5 and v=3.5, then according to (5) (10) Table 3 shows some performances using (9) and Kaiser window method. …”

Section: Three Weights Examplementioning

confidence: 99%

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An efficientway of obtaining formulas of narrowband FIR digital filters based on sinc sum function

Wang

2009

2009 2nd IEEE International Conference on Computer Science and Information Technology

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A new approach is put forward for obtaining formulas of narrowband lowpass FIR digital filters(NLFDFs) with linear phase based on sinc sum function. Five NLFDF formulas are deduced as examples with stopband attenuation from 47dB to 90db and corresponding relations between filter order and transition width are given. Filter orders designed using four formulas are at least 8.2℅ smaller than the ones designed using Kaiser window with same stopband attenuation and same transition width and using the remaining formula even 27℅ smaller. For the design of filters calculation using Kaiser window is incomparable with the calculation of these formulas because the later is not more difficult than calculation using fixed window. In addition, by the same steps as the examples much more NLFDF formulas can be obtained with different stopband attenuation and good performances. IntroductionAbout the NLFDF design with linear phase there are some methods available. We can use fixed window method[1], which is the simplest one, but the order of filters is big. Using Kaiser window and Chebyshev window[1,2] method, we can design filters with relative good performances, but the calculation is some large. About the frequency sampling method, which is suitable for narrowband filter design indeed, but the transition width is some large [1]. As to the optimal method, filter order is almost the smallest in comparison by other types of filters because of equal passband ripple and equal stopband attenuation, but the calculation is very complicated. The three methods are common methods for FIR filter design [1]. In addition we have other methods for selection. Narrowband frequency sampling FIR filters using Zwindow[3] need significantly smaller number of terms than the standard window technique with sharp cut-off amplitude characteristic, it is only suitable for the stopband attenuation in the range of 18-42 dB. The frequency masking technique(FRM) is mainly for the design of narrowband filter [4,5].The basic idea behind the FRM technique is to compose a sharp FIR filter using several short subfilters. There are two sectors in an FRM approach. The first sector forms the sharp transition band and arbitrary bandwidth by a pair of complementary interpolated bandedge shaping filters, whereas the second sector removes undesired periodic frequency components from the bandedge shaping filters by

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“…(ii) let K=2, select 3 points v=0, v=2.5 and v=3.5, then according to (5) (10) Table 3 shows some performances using (9) and Kaiser window method. …”

Section: Three Weights Examplementioning

confidence: 99%

“…Because the primary operations in the technique are decimation and interpolation, its main absence is that calculation for designing filters is complexity. In the design of FIR digital filters the author has developed a new method based on sinc sum function [9]. As an application of the method a new approach to NLFDF design is obtained.…”

Section: Introductionmentioning

confidence: 99%

An efficientway of obtaining formulas of narrowband FIR digital filters based on sinc sum function

Wang

2009

2009 2nd IEEE International Conference on Computer Science and Information Technology

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“…Consequently, windows with good performances can not easily be obtained because for finding satisfied windows three performances of passband, stopband and transition width of lowpass filters must be given attention to simultaneously. In the study of FIR filter design, a new function is defined as sinc sum function [14] by the author. The function has been used in the design of FIR filters, such as lowpass filters [14] and differentiators [15,16].…”

Section: Introductionmentioning

confidence: 99%

“…In the study of FIR filter design, a new function is defined as sinc sum function [14] by the author. The function has been used in the design of FIR filters, such as lowpass filters [14] and differentiators [15,16]. Further study shows that it can be used in the design of FIR HT.…”

Section: Introductionmentioning

confidence: 99%

An Application of Sinc Sum Function in Hilbert Transformer

Wang¹

2013

ENG

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An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT are proved by using the properties of the sinc sum function. A general HT formula is obtained theoretically and it contains a general window function. As an example three new window functions are obtained. Different from the existing window func- tions obtained from lowpass filters, these window functions are obtained directly from HT. Comparisons show that new windows are better than the Hanning, Hamming, Blackman and Kaiser windows in terms of HT performances.

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“…This is partly because continuous -time filter design was highly advanced art before discrete-time filters were of interest [1]. In [2] different windows has been given with their classification such as fixed, adjustable window functions, weight windows based on Atomic functions, polynomial windows and, Z-window functions. In [3], three different window functions Han window, Hamming window and Blackman window in a general format according to evolutionary algorithm has proposed.…”

Section: Introductionmentioning

confidence: 99%