Let f(t) be a bandlimited Fourier series defined with fundamental period T = 1. That is,...

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Let f(t) be a bandlimited Fourier series defined with fundamental period T = 1. That is, b f(t) = a[k] exp(j2πkt), t= [0, 1] k=-b where a[k] are the Fourier series coefficients of f(t). From an experiment, f(U₁),..., f(Un) are obtained where U₁,..., Un are given i.i.d. realizations of a Uniform [0, 1] random variable. Knowing the values of U₁,..., Un develop an approximation for the Fourier series coefficients a[k]. Evaluate the mean-squared error of your approximation for a[k]? It would be desirable if the mean-squared error decreases to zero as no. Let f(t) be a bandlimited Fourier series defined with fundamental period T = 1. That is, b f(t) = a[k] exp(j2πkt), t= [0, 1] k=-b where a[k] are the Fourier series coefficients of f(t). From an experiment, f(U₁),..., f(Un) are obtained where U₁,..., Un are given i.i.d. realizations of a Uniform [0, 1] random variable. Knowing the values of U₁,..., Un develop an approximation for the Fourier series coefficients a[k]. Evaluate the mean-squared error of your approximation for a[k]? It would be desirable if the mean-squared error decreases to zero as no.

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