e All of the cont,inuous and discrete signals that, we have considered so far in the timeclomain arid freqitcnry-doincri W P L ~ signals that could be described by xiiatli- ematical lunc
Trang 1e
All of the cont,inuous and discrete signals that, we have considered so far in the timeclomain arid freqitcnry-doincri W P L ~ signals that could be described by xiiatli- ematical luncIions 1% could calculate the valoes of the signal, add and subtract signals, clday signals and torrn derivatives ancl integrals We found integration vcry uscful, foi convolution, for Fourier arid Laplace tiansfornis, ~ n t l wc~ also u s t d complex iiitegrrttion for the inverse Laplace and inverse z-transfornris For discrete signals summation is iised in d of irittegration Shis was all possiblc bcc*ause
we l m l assiimcd that every s I had one definite value at avenj’ poiiit in time,
md t h a t every signal coiilil he described by a mathematical formula, however complicated that formula might be
M M L ~ signals that occur in practise do not conform to this assumption It
~voulcl be theoretically possible to desrribe the sprcch signal from Figure 1.1 wit 2.1
the properties of the human vocal tract by superiiiiposirig various waves, but this would not lead to a tecliiiically realistic solution It is cornpletely impossible to assign functions to iioise signals, or Sigriiils made np of c ascillations A i i ~ w coiiccpt nnist be found to represent such irregular pro Just unclerstwding that, a signal waveform can have aii uiiprcdictablc val is t h c b r efore rtid[)IT1,
does not actually help much To deal with system inputs and outputs in the way we are nsed to, random signals must he described by non-random or ‘deterministic’ quantities This can be prrtorrn.d by the so-called expected values, which arc iritrodncc~d in t h e next section Then we will cleal with stationary and ergo&; raiidoni processes, for w2iich a significantly simpler calculation i s possi blt with cxpertetl valuts, An important clabs of exp tl values arc correlation functions
which will also be disc-ussad All of tlicsc forms for describing random signals will
be introduced for continuous signals, a i d the chapter concludes by cxteudiiig t h t concepts to dibcrete rantloni signals
.1.1 at Are Ran
The signals that we have been working with 60 far are called ddernimzstzr sz.gnala, which means that a signal has a ksiowri unambiguous value at every poiiit ill
time A signal ctui also be deterministic when it cannot, he described by siinple
mathematiral functions but i i i s t e d for example, by an iiifiiiite Fourier series,