Consider computingthe Laplace transform of a pulse:
p(t) = {1 0 < t < 1
{0 otherwise
a) use the integral formula to find P(s), the Laplace transform of p(t). Determine the region of convergence of P(s).
b)Represent p(t) in terms of the unit-step function and use its Laplace transform and the time-shift p

I have attached some problems that I think I am working correctly. I wanted to verify the concept is correct.
A signal x(t) = exp(-t)*cos(3t) is turned on at t = 0. What is its Fourier transform?
Consider the signal in problem 6. What is the Fourier transform of its derivative with respect to time?
What is the Fourie

1. Calculate the Laplace transform of exp(-10t) x u(t)
2. Calculate the convolution of exp(-t) and sin(t) using (a) the Laplace transform (b) direct integration
3. Compute the inverse transform of (3s^2 + 4s + 1) / (s^4 + 3s^3 +3s^2+2s)
4. Use Laplace transform to calculate the solution to the ODE y"+6y'+8y=u(t) y

1. For a discrete-time signal x[n] with the DTFT where b is an arbitrary constant compute the DTFT V(Ω) of v[n] = x[n] - x[n-1].
2. Compute the rectangular form of the four-point DFT of the following signal, which is zero for n<0 and n>=4.
3. Compute the inverse DTFT of: X(ω)=sinΩ cosΩ
4. Compute the inverse DTFT of

Attached are three problems that I am working. Any assistance would be greatly appreciated.
For a discrete-time signal x[n] with thez-Transform:
X(z) = z
________________________________________8z2-2z-1
find thez-Transform, V(z) for the signal v[n] = e3nx[n].
See attached for the rest of the

Please see attachment.
1. What is the Fourier Transform for the convolution of sin(2t)*cos(2t).
2. Compute the inverse Fourier transform for X(w)= sin^2*3w
3. A continuous time signal x(t) has the Fourier transform
X(w) = 1/jw+b where b is a constant. Determine the Fourier transform for v(t) = x*(5t-4)

Any causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the j? axis) has, as we saw before, a region of convergence that includes the j? axis, and as such its Fourier transform can be found from its Laplace transform. Consider the following signals:
x1(t) = e^-(2t) * u(t)
X

Please see the attached file for full problem description.
16. Compute the inverse Laplace transform of X(s) = (s + 2)/(s^2 + 7s + 12)
17. The Laplace transform of e^(-10t)*cos(3t)u(t) is
18. Use the Laplace transform to compute the solution to the differential equation defined by dy/dt + 2y = u(t) where y(0) = 0.
19