DocumentCode :
957760
Title :
Recursive filters with uniform power distribution
Author :
Kurshan, R.P. ; Odlyzko, A.M.
Author_Institution :
Bell Laboratories, Murray Hill, USA
Volume :
16
Issue :
17
fYear :
1980
Firstpage :
672
Lastpage :
673
Abstract :
Recursive linear digital filters which operate without roundoff errors, known as cyclotomic filters, have been shown to be useful as tone generators and detectors applicable to pseudo-random noise generation. Touch Tone®, f.s.k. and broadband frequency detection. These filters are modelled by periodic linear recursions with integer feedback coefficients. In certain applications, such as tone detection, it is desirable to have considerable differentiation between the detected and the rejected frequency amplitudes. Other applications such as pseudorandom noise generation require a more uniform power distribution throughout the spectrum. It is shown that the number N(m) of distinct nonzero spectral amplitude levels for such a filter of period m is exactly N(m)=¿(m0)/2 when in m0>2, where m0 is the largest square-free divisor of m and ¿(m0) is the number of positive integers less than and sharing no prime factor with in m0; N(m)=1 when m0¿2. In particular, a uniform power distribution is effected over the entire spectrum of resonating frequencies (i.e. N(m)=1) if and only if m=2a3b for some non-negative integers a and b.
Keywords :
digital filters; spectral analysis; cyclotomic filters; detectors; power distribution; pseudorandom noise generation; recursive digital filters; spectral amplitude levels; tone generators;
fLanguage :
English
Journal_Title :
Electronics Letters
Publisher :
iet
ISSN :
0013-5194
Type :
jour
DOI :
10.1049/el:19800476
Filename :
4244250
Link To Document :
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