alculated as 20.67 and from Table 1.3 it is seen that the results Dunn, R.A. and Ramsing, K.D. (1981) Management science, a are highly significant since there is a very low probability, less than practical approach to decision making, Macmillan. 0.5%, that it can arise by chance. Fitzsimmons, J.A. (1982) Service operations management, McGraw-Hill. 1.11.3 Significance of correlation Grant, E.I. and Leavenworth, R.S. (1980) Statistical quality control, McGraw-Hill. The significance of the product moment correlation coefficient of Hahn, W.C. (1979) Modern statistical methods, Butterworths. Equations 1.19 or 1.20 can be tested at any confidence level by Jones, M.E.M. (1988) Statistics, Schofield & Sims. means of the standard error of estimation given by Equation 1.21. Mazda, F.F. (1979) Quantitative techniques in business, Gee & Co. An alternative method is to use the Student t test of significance. Siegel, A.F. (1988) Statistics and data analysis, Wiley. This is given by Equation 1.57, where r is the correlation coefficient Taylor, W.J. and Watling T.F. (1985) The basic arts of management, and n the number of items. Business Books. This page intentionally left blank Fourier analysis William J Fitzgerald University of Cambridge Contents Introduction 2/3 Generalised Fourier expansion 2/4 Fourier transforms 2/6 Discrete sequences 2/7 The discrete Fourier transform 2/8 The inverse discrete Fourier transform 2/9 The fast Fourier transform 2/9 Linear time-invariant digital systems 2/10 The inverse z-transform 2/15 Data truncation 2/16 Conclusions 2/17 References 2/17 This page intentionally left blank Introduction 2/3 2.1 Introduction (2.4) This chapter considers Fourier analysis and associated transform methods for both discrete-time and continuous-time signals and This will, in general, be in error since it is only a representation of systems. Fourier methods are based on using real or complex sinu- the function f(t), and we will require that the representation should soids as basis functions, and they allow signals to 