Between the DFT Bins

• Recall that DFT sinusoids are integer multiples of the sampling rate divided by N
  $$f_k = k\frac{f_s}{N}, k = 0, 1, 2, ..., N-1.$$

• The DFT sinusoids are the only frequecies that have a whole number of periods in $N$ samples.

• Consider the periodic extension of a sinusoid lying between DFT bins (see Matlab script betweenBins.m).

  Figure 8: ``Glitch'' corresponds to spectral artifacts.

  

• Notice the ``glitch'' in the middle where the signal beings its forced repetition. This results in spectral ``artifacts''.