Step 1: Understand the discrete Fourier representation
The discrete Fourier representation of a signal $x[n]$ is given by:
\[ X[k] = \sum_{n=0}^{N-1} x[n] e^{-i 2\pi k n / N} \]
where $N$ is the total number of samples in the signal, $k$ is the frequency index, and
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