.

Include unity circle and exterior of circle hence x(z) will be stable, causal.

£f(t) =

£^-1F(s) = f(t)

£[a f₁(t) + bf₂(t)] = aF₁(s) + bF₂(s)

where

£[f(t - T)] = e^-sT F(s)

£[e^-at f(t)] = F(s + a)

Initial value theorem

Final value theroem

Convolution Integral

where t is dummy variable for t.

For causal output must depend upon Present and past not on future.

.

The probability that first ball is white is and the probability the second ball is white is . The probability that both are white is .

Add elements individually.

£e^-at f(t) = F(s + a).

Because to design band pass or band stop, transfer function of must be second order.

The simplest method to find the ROC. Put denominator to greater than zero.