DocumentCode :
1095381
Title :
A parameter estimation approach to estimation of frequencies of sinusoids
Author :
Chan, Y.T. ; Lavoie, J. M M ; Plant, J.B.
Author_Institution :
Royal Military College of Canada, Kingston, Ontario, Canada
Volume :
29
Issue :
2
fYear :
1981
fDate :
4/1/1981 12:00:00 AM
Firstpage :
214
Lastpage :
219
Abstract :
It is shown that with uniform sampling, a sample of the sum of M sinusoids at time nT can be uniquely expressed as a linear combination of the 2M samples at times (n - 1)T,..., (n - 2M)T. The 2M coefficients of linear combination are also the coefficients of a 2M-order polynomial whose roots are 
being the frequencies of the sinusoids. Given the samples of sinusoids plus noise, a consistent estimate of the 2M coefficients are obtained by the instrumental variable method of parameter estimation. It is also possible to track time-varying frequencies by a recursive algorithm that exponentially weighs out the past data. Simulation examples of one and two sinusoids are given.
being the frequencies of the sinusoids. Given the samples of sinusoids plus noise, a consistent estimate of the 2M coefficients are obtained by the instrumental variable method of parameter estimation. It is also possible to track time-varying frequencies by a recursive algorithm that exponentially weighs out the past data. Simulation examples of one and two sinusoids are given.Keywords :
Autocorrelation; Frequency estimation; Helium; Instruments; Parameter estimation; Phase estimation; Polynomials; Recursive estimation; Sampling methods; White noise;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1981.1163543
Filename :
1163543
Link To Document :
