Analytic Signals (Advanced Signal Processing Toolkit)

Note  This topic contains information that applies to the LabVIEW Time Frequency Analysis Tools.

For real-valued signals, the power spectrum has symmetric components at positive frequencies and at negative frequencies. The corresponding analytic signal of the real-valued signal is a complex-valued signal. The analytic signal retains the DC component of the real-valued signal, doubles the components with positive frequency, and removes the components with negative frequency. The following illustrations show the power spectrum of a real-valued signal, s(t), and the power spectrum of the corresponding analytic signal.

Notice that the power spectrum of the real-valued signal is symmetric about 0 Hz. In comparison, the power spectrum of the analytic signal is not symmetric and contains components with positive frequency only. Furthermore, the amplitude of the power spectrum of the analytic signal with positive frequency is twice the amplitude of the power spectrum of the real-valued signal. Whereas the amplitude of the power spectrum of the real-valued signal is 40 at 300 Hz, the amplitude of the power spectrum of the corresponding analytic signal is 80 at 300 Hz.