213 9.6 Iwerse Fourier Transform four tcrrns in totsal for the time signal, and also the spectrum The symmetry relationships (9.55), (9.56) for real signals can be iisetl for thc real part, and (9.59), (9.60) for imaginary sigiials can be used for the imaginary part The sclieriie (9.61) can be formed from these, for tlie symmetry betwccn real and imaginary parts of the even aid odd parts of a timr signal arid spcctrum 1191 Although the syiiimetries seem to get more and more complicatled, in fact, tlie gener it1 complex case is sinpisingly simplc, logical, and easy to remeniber Example 9.6 A complex signal ~ ( thas ) t h e Foirier trimsform X(ju).What is 3{x * ( t ) } ? Tt can be tsakeIifrom (9.61) that changing the sign of the iiiiagiriary part in thc time-domain lias the following efkct in Lhe freciiiency-domain: F{a*(L)}= Re(X,(jw)} - Re(X,,(jw)} - jIm{Xe(jw)} + jIni{Xf)(jw)) Using t , h syrrirrietry of tsbceven ancl odcl parts this c:a8nba wri + F{,c*(t)} = Kc{X, ( - , j ~ ) } Re{&,(-jw)} - jIrn{X,(-jw)) = X*(-jw) more concisely: gTrn(X,(-gw)} * Equation (9.61 yields tbc' important transforni pair The iriverse of the Foiirier transform is an iiitcgral expression that ha:, a lot of similarity with thr Foirrier integral (9.1);