| 35.1 |
DFT of a Sinusoid (contd..) |
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Substituting
xk from (3) in (6) and (7) it can be shown that for a sinusoidal
input signal given by (1) |
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Therefore, from equation (2), (5) and (8) it follows that |
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When the input signal contains other frequency components as well, the phasor calculated by equation (9) is a filtered fundamental frequency phasor. It is presumed here that the input signal must be band-limited to satisfy the “Nyquist Criterion”, to avoid errors due to aliasing affects. |
| 35.2 |
Phase Computation using DFT |
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In relaying applications, during steady state, we will be working with a moving window, such that each window is having N-most recent samples. Let  and  indicate  and  component of DFT for  window. By our convention, window number is the sample number of the first sample in the active window. As the first N - 1 windows are incomplete, there window number is one. Afterwards, window number is incremented by one for each new sample. |
