Using Laplace can someone please show me in simple terms how i would solve the following function? This is a lecture example. The solution just shows the answer, nothing about how we get it or what it represents. I am finding this subject particularly difficult to come to grips with. δ(t-1) Can you also explain what the function represents? Thanks mm
δ(t-1) is an impulse at t=1, so it has no value at other values of time it represents a rectangular pulse of area = 1 the width of the impulse is very narrow, approaching 0.00 nanoseconds which means its height is correspondingly high, tending to infinity. In practice, a realistic approximation to the delta function is plenty good enough for testing the impulse response of real-world systems. Sorry, I can't relate it to Laplace, I have forgotten the topic through disuse. Try searching google.
The key point to know when computing the laplace of the dirac delta function is that the ∫[f(t)*δ(t-ε)]dt from {0 to t} = f(ε) because δ(t-ε) = 0 everywhere except ε and ∫(δ) from {0 to ∞} =1.