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

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

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

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

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

When x(t), the input to N, is known, and when h(t),the impulse response of N, is known, the y(t), the output or response function, is expressed by

15-5 Several basis theorems for the Laplace transform 1.The linearity theorem{fi(t)+()}=()+(s) Example:

When initial energy is present in a circuit, the Laplace transform method may be used to obtain the complete response. The first is the more fundamental, for it involves writing the differential equations for the network and then taking the Laplace transform of those equations

You are asked to set off from any piece of the lands and pass through all the seven bridges under the condition that each bridge can be used only once, so that you can finally return to the starting point

Augmented loop matrix +1when branch b; is in loop lk and has the same orientation; B. =]; ={-1 when branch b; is in loop lk and has the opposite orientation; when branch; is not in loop lk