Final answer:
The student needs to perform a Fourier series expansion for a discrete-time signal composed of spaced delta functions. This involves computing the Fourier coefficients using the appropriate formula and constructing the series based on the coefficients obtained. For this signal, the periodicity is three units apart, thus N is chosen as 3.
Step-by-step explanation:
The student is asking how to derive the Fourier series expansion for a discrete-time signal x[n]=∑⁺[infinity] ₖ₋∞ δ[t−3k]. This signal appears to be an infinite sum of delta functions spaced three units apart in time. The Fourier series expansion of a periodic signal is a way of expressing the signal as the sum of sinusoidal functions. We can derive the Fourier series coefficients for this signal by using the formula for Fourier series coefficients in discrete time:
ak = (1/N) ∑N-1n=0 x[n] e-j(2πkn/N), where N is the period of the signal and k is an integer index for the harmonics.
In this case, N would be 3 since the delta functions are 3 units apart. By substituting into the formula and evaluating the sum, the coefficients ak can be determined, enabling the construction of the signal's Fourier series representation.