A signal x (t) = e-btu(t) is given as an input to a system with unit h(t) = e¯atu(t) impulse response a. If x=5, b=2, find the c signal obtained at the output with the following methods. www a) Find by calculating the convolution of x(t) and h(t) in the form y(t)=x(t)*h(t). b) Calculate the inverse Fourier transform of the product of the Fourier transforms of x(t) and h(t) in the form y(t)=F¯{H(jw)X(jw)}.

Find the Fourier transform of the function x(t), below. x(t) = 10e-2u(t)

Solve correctly please

You are an electrical engineer now and are receiving a communication signal. You find that the signal can be formulated as f(x) =[8(x-2)+8(x+2)] (1) Your team leader asks you to analyze the result of the particle movement in the frequency domain. You first decide to apply the Fourier Transform to do this job. Please show your result after applying the Fourier Transform. (2) While receiving the signal, you adopt a circuit to process this signal. After your analysis, you can model the circuit by using the following ordinary differential equation (ODE). Please solve it. y'(x)+3y'(x)+2y(x) =[8(x-2)+8(x+2)] 2i

Find the Continuous Time Fourier Transform of the following signal