notes_harris_paper - PROCEEDINGS O F THE IEEE VOL 6 6 NO 1...

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PROCEEDINGS OF THE IEEE, VOL. 66, NO. 1, JANUARY 1978 51 On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform FREDRIC J. HARRIS, MEMBER, IEEE Ahmw-This Pw!r mak= available a concise review of data win- compromise consists of applying windows to the sampled daws pad the^ affect the Of in data set, or equivalently, smoothing the spectral samples. '7 of aoise9 m the ptesence sdroag bar- The two operations to which we subject the data are momc mterference. We dm call attention to a number of common -= be rp~crh windows den used with the fd F~- sampling and windowing. These operations can be performed transform. This paper includes a comprehensive catdog of data win- in either order. Sampling is well understood, windowing is less related to sampled windows for DFT's. I. INTRODUCTION HERE IS MUCH signal processing devoted to detection and estimation. Detection is the task of determiningif a specific signal set is present in an observation, while estimation is the task of obtaining the values of the parameters describing the signal. Often the signal is complicated or is corrupted by interfering signals or noise. To facilitate the detection and estimation of signal sets, the observation decomposed by a basis set which spans the signal space [ 11. For many problems of engineering interest, the class of signals being sought are periodic which leads quite naturally to a decomposition by a basis consisting of simple periodic func- tions, the sines and cosines. The classic Fourier transform is the mechanism by which we are able to perform this decom- position. By necessity, every observed signal we process must be finite extent. The extent may be adjustable and selectable, but it must be finite. Processing a finite-duration observation imposes interesting and interacting considerations on the har- monic analysis. These considerations include detectability of tones in the presence of nearby strong tones, resolvability of similarstrength nearby tones, resolvability of shifting tones, and biases in estimating the parameters of any of the afore- mentioned signals. For practicality, the data we process are N uniformly spaced samples of the observed signal. For convenience, N is highly composite, and we will assume N is even. The harmonic estimates we obtain through the discrete Fourier transform (DFT) are N uniformly spaced samples of the associated periodic spectra. This approach is elegant and attractive when the processing scheme is cast as a spectral decomposition in an N-dimensional orthogonal vector space [ 21. Unfortu- nately, in many practical situations, to obtain meaningful results this elegance must be compromised. One such Manuscript received September 10, 1976; revised April 11, 1977 and September 1, 1977. This work was supported by Naval Undersea Center (now Naval Ocean Systems Center) Independent Exploratory Development Funds.
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This note was uploaded on 03/16/2012 for the course ECEN 487 taught by Professor Dr.brianjeffs during the Winter '12 term at BYU.

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notes_harris_paper - PROCEEDINGS O F THE IEEE VOL 6 6 NO 1...

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