You have seen that the DFT or FFT of a real signal is a complex number, having a real and an imaginary part. The power in each frequency component represented by the DFT/FFT can be obtained by squaring the magnitude of that frequency component. Thus, the power in the kth frequency component, the kth element of the DFT/FFT, is given by |X[k]|2. The plot showing the power in each of the frequency components is known as the power spectrum. Because the DFT/FFT of a real signal is symmetric, the power at a positive frequency of kf is the same as the power at the corresponding negative frequency of k
f, excluding the DC and Nyquist components. The total power in the DC and Nyquist components are
and
respectively.
Because the power is obtained by squaring the magnitude of the DFT/FFT, the power spectrum is always real. The disadvantage of this is that the phase information is lost. If you want phase information, you must use the DFT/FFT, which gives you a complex output.
You can use the power spectrum in applications where phase information is not necessary, for example, to calculate the harmonic power in a signal. You can apply a sinusoidal input to a nonlinear system and see the power in the harmonics at the system output.
You can use the Power Spectrum VI located on the Functions»Analyze»Signal Processing»Frequency Domain palette to calculate the power spectrum of the time domain data samples. Just like the DFT/FFT, the number of samples from the Power Spectrum VI output is the same as the number of data samples applied at the input. Also, the frequency spacing between the output samples is f = fs/N.