1) Compute tan(i) where i = −1.
2) Convolve χ[0,2](t) with tU(t). Evaluate the integrals and plot the result.
3) Compute the Fourier transform of te−3tU(t). Hint: Use an integral table to evaluate the integral..
4) Let us have a function f(t) whose Fourier transform is F(ω). Prove that the Fourier transform of
5) Consider a signal f(t) whose Fourier Transform is f(ω) = χ[−100,100](ω). We want to sample this signal. What is the lowest rate of sampling we can use if we dont want any aliasing?
6) Filter the signal
1 2 4 1 2 0 4 3
1 1 1 1
1 0 4 2
with the filter
1 0 1 0 2 0 1 0 1
Use zero boundary conditions.
