Imperfections in a sampler cause characteristic artifacts in the sampled signal. In this problem we will look at the case where the sample timing is non-uniform, as shown below: The

sampling function f(t) has its odd samples delayed by a small time T. (a) Write an expression for f(t) in terms of two uniformly spaced sampling functions. (b) Find F(jw), the Fourier transform of f(t). Express the impulse trains as sums, and simplify. (c) Find F(jw), for the case where ↑ = 0, and show that this is what you expect. (d) Assume the signal we are sampling has a Fourier transform Sketch the Fourier transform of the sampled signal. Include the base band replica, and the replicas at w = ±n. Assume that t is small, so that EIWT ~1+ jwT (e) If we know g(t) is real and even, can we recover g(t) from the non-uniform samples g(t)f(t)? .