Types of Periodic Functions and Non Periodic Functions 
and Their Representation by Discrete and Continuous Spectra 
Actual wave record n= Malt) 
a 
t=0 t=t, t=t> t=ts 
| | minute | 
Analysis no. | Purely periodic with one discrete 
spectral component. 
At n(t) = A,cos nee =eANICOS it (3.1) 
| 
n,(t) 7 n(t+7,) (3.2) 
By A 
Portiioni off graphy mori 7) ite 1a Neu 000 
Analysis no. 2 Purely periodic with many discrete 
spectral components. + (3.3) 
A no(t) = = Ancos(2=mt A py) e = NGOS (rahi S Sp)! 
ee esi) aca) (3.4) 
Une 2 cine) en = a (3.5) 
Portion of graph of 7(t) 
Analysis no. 3 Not periodic with a continuous spectral 
representation. 
Col 1) na(t) = folt) + f,(t-t)) + fo(t-tg) + fa(t-ts) (36) 
Ga(ne= Lf folt)cosptdu bolu) = tf folt)sinutdy (3.7) 
folt) = foo(u)cosutdy +f bo(u)sinutdy (3.8) 
Co(p) = + VGou)® + (Don)*® (3.9) 
VV pe 
Graph of 43(t) 
PLA Je 
Si 
