equations with const,mt coefficients Studying IXl-systems over a frequency r,mge (Chapter ) 1ea.ds11s to the reprcsentation of continiious-time signals with the help of the Laplac:(: transform, whi.ch svc discuss in detail in Chaptrer Chapter presents the inverse forrnultz of the Laplace transform and its fundamentals in complex function theory The analysis of LTIsyst,erns with the Laplace t,ransforai and its cliasa ris&,i(jn via, thc syst c ~ i itiinc%ioii is the subject of Chapter Although linear differential equations with consta.nt coefficients arid specified start, sralues are no longer LT1-systems, LTI methods can be elega-ntky exteaded for this important class of prohlems (Chapter 7); this occurs primwily via system description in Another kind of characterisation of LTI-systems i the impulsc rcsponse is discussed in Chapter In order to be ablc to describe the impulse response mathematica.lly, we introduce generalised functions in this context An inr,egral transforniation cqual in iniporttialce to thc Laplace tramform is the Fourier transform, whose characteristics and laws are discussed in Chaptcr The graphi.cal analysis of the Gequericy rt.;sponse of systems by means of Bode cliagra.ms is the snhj Chapter 1.:I concerns sa.mpledand periodic signals as wcll as the sampling theorem and leads u s to discrote-time signals and their Fourier spectrum (Chpter 12) In Chaptcr 13 we handle discrete signals with thc x-tramform, the discrete counterpart of t,he Laplace transformation, arid in Chapter 14 we use it to mialyse discrete-time LTI-systems In the subsequent chapters continuous axid discrete systems and signal: arc treated in combination The characteristics of causal systems and signals and their description with the I-filbert transforma.tion is the subject of Chapter 15, and Chapter 16 prcscnts st.ability characteristics ol systerns In Chapter 17 we introduce random signals and their description via expectcd \dues; in a,ddit,ioii,,we discuss a frequency response representation of rniidom signals via power derisily spectra Finally, Chapter 18 is dcclicltted to the yuestiori of how expected vdues and power density spectra are, modified by LTI-systems Exercise 1.1 Are the fdlowirig sign& ;i mpl i t iiti+cli scwtc cli scrot e-t irnc itnd / or digit d'! aj nitmber of days of rain per inonth b) average high tcinpcrature per month c) current tcmpcraturc II