1. Show that the rotation property of DFT. For x = r cos θ, y = r sin θ, µ = ω cos ψ, ν = ω sin ψ f(r, θ + θ0) ↔ F(ω, ψ

[answerhappygod]

1. Show that the rotation property of DFT. For x = r cos θ, y =
r sin θ, µ = ω cos ψ, ν = ω sin ψ
f(r, θ + θ0) ↔ F(ω, ψ + θ0)
2. Suppose that you have f(x) and g(x) whose lengths are M and N
respectively. You have zero-padded the two sequences so that the
zero-padded sequences have length M + N − 1. Show that the M + N −
1 point inverse DFT of the product of M + N − 1 point DFTs of the
zero-padded sequence is the same as the linear convolution of f(x)
and g(x).
3. Suppose a band-limited signal f(x) is sampled with sampling
period T. Determine the continuous time Fourier transform of the
sampled signal.