CONTENTS 
Page 
FOREWOR, eis ec its ST el AN ale a era wie iy lila ola Ai xix 
Preface: 0.08050 RE ROR NN CUA CO er eg aca tmtapaa bau) UN Rk XX1 
Abstract (5 00) 205 Tae in ya Wee erate 1 
Chapter 1 Introduction (77 2755) 2 2 ee neat iota Salt 2 
UT VPEOLO RG ee oo Sic sig SIA aa os leek a I le NO Z 
1.2 Pursuing the Improvement of CoherencysFunctionss eee eee 3 
J’ 3) ‘Mime Domain Characteristics! 4.15. eee ee 3) 
14> Treatment of Nonlinearitiesy.sneaee ee hee ee en 4 
1.5, Scope:of Studies case le ics esky Bie eee edn Oh Ue Up a 4 
Part I 
A Review of Spectral Analysis Through Periodogram 
(Nonparametric Spectral Analysis) ................. 00-0 ccceeeeec cece ee. 5 
Chapter 2 Basic Procedure of the Spectral Analysis and the 
Problem of Sample Computations ........................... 5) 
2.1 Random Process and Its Characteristics ..................-........... 5 
2 Il Completely Stationaryig ser). ae eee ee ee 6 
2.1 2 Stationary \Up'to|Orderim aes ne oan ON NYS 6 
2.13 Stationary Up'to Order, 2isc. sais wsceh ie Aes eee eT 6 
2d. A Er godicity ries «siatsce spin’ pceelel Mb RAR ohaces 20 Gana eel ues Bin Mule 2 6 
2.1.5 Summary of Gaussian (Normal) Probability Distribution Functions ..... 7 
2.2 Properties Required for Estimator ...........022¢2¢2s0e.c200-0...... 9 
22:1 sUnbiasedness ac eins vals: cee On ee Mee) 9 
22-2 High Relative Efficiency.) ..\1 0.154. ee. ee 9 
22.3 SmalliMean Square!Errors. pins i ee oe 9 
22-4 \CONSIStENCY) .. .'..1s souk SANE ike hoe ea Ot Te er 10 
22S SUPICIONCY) 5 iansaieuls ih saresa hs pete TR ae EE Re LP 10 
2.3 Autocovariance Function and Its Estimates ........................... 10 
2:31 Estimates OF Rr) oo sos os veces ohne eee 11 
23-2 Unbiased Estimate: iso ces sec Lee OEE 11 
23.3 Biased Estimate see «i soos ajnss sees tn als oy.) eee eR EA 11 
24, Spectrum:Analysis. ..0\ i4<chyethe Aan oo Nek ey yee ae alse 12 
241 Spectrum yor, Various | Processes py vin ne ee en ee 12 
2.4.2 Spectral Representation of the Stationary Random Process............ 19 
2.4.3 Spectrum of Discrete Parameter Process, Aliasing .................. 20 
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