
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

Discrete WirtingerType Inequalities for Gauging the Power of Sinusoids Buried in Noise
Saed SAMADI Kaveh MOLLAIYAN Akinori NISHIHARA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E92A
No.3
pp.722732 Publication Date: 2009/03/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E92.A.722 Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing) Category: Keyword: discrete Wirtinger inequalities, FanTausskyTodd inequalities, sinusoids, spectrum analysis, maximally flat filters, circular convolution, additive white noise, signaltonoise ratio,
Full Text: PDF>>
Summary:
Two discretetime Wirtingertype inequalities relating the power of a finitelength signal to that of its circularlyconvolved version are developed. The usual boundary conditions that accompany the existing Wirtingertype inequalities are relaxed in the proposed inequalities and the equalizing sinusoidal signal is free to have an arbitrary phase angle. A measure of this sinusoidal signal's power, when corrupted with additive noise, is proposed. The application of the proposed measure, calculated as a ratio, in the evaluation of the power of a sinusoid of arbitrary phase with the angular frequency π/N, where N is the signal length, is thoroughly studied and analyzed under additive noise of arbitrary statistical characteristic. The ratio can be used to gauge the power of sinusoids of frequency π/N with a small amount of computation by referring to a ratioversusSNR curve and using it to make an estimation of the noisecorrupted sinusoid's SNR. The case of additive white noise is also analyzed. A sample permutation scheme followed by sign modulation is proposed for enlarging the class of target sinusoids to those with frequencies M π/N, where M and N are mutually prime positive integers. Tandem application of the proposed scheme and ratio offers a simple method to gauge the power of sinusoids buried in noise. The generalization of the inequalities to convolution kernels of higher orders as well as the simplification of the proposed inequalities have also been studied.

