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Discrete Frequency Axis

Understand how discrete frequency axes are formed from N time-domain samples and why only N unique complex sinusoids exist. Learn the relationship between discrete frequency indices and continuous frequency, sampling of the frequency axis, and the implications for digital signal analysis.

With NN discrete time domain samples, there are only NN complex sinusoids that are orthogonal to each other for k=0,1,2,,N1k=0,1,2,\cdots, N-1.

The other option is k=Nk=N, which we’ll investigate next.

Frequency index: k=Nk=N

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