Recent content by redundant6939

The region of convergence then, would it be btw the two values of s?

The LT of ##y'(t)## and ##y''(t)## are sY[s} and ##s^2Y## respectively. I am not sure what you mean exactly.

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Homework Statement Find the inverse Fourier transform of X(ejw = 1/(1-ae-jw)2 using the convolution theorem. Homework EquationsThe Attempt at a Solution I tried finding the partial fraction coefficients but without success.

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = \frac{s}{s^2+9π^2} L(h(t)) = \frac{1}{s+2} I then try to find the partial...

But isn't that the LT of cos(3pi*t)u(t)?

Is it \frac {s}{s^2 + (3π)^2} ?

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = [πδ(ω - 3π) + πδ(ω + 3π)] L(h(t)) = \frac{1}{s+2} Laplace Transform inverse ...

Find the LT and specify ROC of: x(t) = e-at, 0 ≤ t ≤ T = 0, elsewhere where a > 0 Attempt: X(s) = - 1/(s+a)*e-(s+a) integrated from 0 to T => -1/(s+a)[e-(s+a) + 1] Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T Elsewhere ROC is empty (LT doesn't exist). Is this...

Homework Statement Find convolution of x[n] (graph in attachment) and h[n] where h[n] = u[n] Homework EquationsThe Attempt at a Solution - flipped the h[n] to have h[-n] - moved to the left once (h[-1-n]) to align - multiplied h and x and it gives me all zeros Is this correct or I'm missing...