Fourier Series Manipulation. Consider a real-valued signal f(f) with the Fourier

Question

Fourier Series Manipulation. Consider a real-valued signal f(f) with the Fourier series representation Some transformations of f(f) can he represented by simply modifying the Fourier series coefficients. Let g(t) be the time-reversed version of f(-t). Let g(t) have Fourier series coefficients, cn. Derive the relationship between the Fourier series coefficients. cn and dn. Let y(f) be the time-shifted version of f(f) represented by y(t) = f(t - t0) for real constant to. Let y(f) have Fourier series coefficients denoted by bn. Derive the relationship between the Fourier series coefficients. bn and dn.

Explanation / Answer

just write the given equation for f(-t) and then compare it with general equation u will find as dn = c-n for part b Substitute t-to in the given formula compare with general equation u will get as bn=dn e-jwto

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