We define the unit impulse as a function of time which is zero when its argument, generally (t-o), is less than zero; which is also zero when argument is greater than zero; which is infinite when its argument is zero; and which has unit area

The two-sided or bilateral Laplace transform The one-sided Laplace transform or direct Laplace transform

14-8 Definition of the Fourier transform The exponential form of the Fourier series

We consider each term of the Fourier aeries representing the voltage as a single source. The equivalent impedance of the network at no is used to compute the current at that harmonic. XL(n) =noL and XC() =-1/noC The sum of these individual responses is the total response i

14-6 Effective values and power The effective or rms value of the function f(t) is

14-5 Waveform synthesis Synthesis is a combination of so as form a whole

14-4 Line spectrum A plot showing each of harmonic amplitudes in the wave is called the line spectrum

1.A functionf(t) is said to be even iff(t)=(-t). They are symmetrical with respect to the vertical axis. (bn=0)

S14-2 Exponential Fourier series f(t)=+ cosot+a2 cos 2ot+.] sinot+ b2 sin

Any periodic waveform f(t)f(t) can be expressed by a Fourier series provided that (1) If it is discontinuous, there are only a finite number of discontinuous in the period T (2)It has a finite average value over the period T (3)It has a finite number of positive and negative maximums in the period T