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Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase ) of a complex-valued function s ( t ), is the real-valued function:
Rotational frequency, usually denoted by the Greek letter ν (nu), is defined as the instantaneous rate of change of the number of rotations, N, with respect to time: ν = dN/dt; it is a type of frequency applied to rotational motion.
The definition of instantaneous frequency is the time rate of change of phase, or (), where () is the instantaneous phase of a signal. We can know the instantaneous frequency from the time–frequency plane directly if the image is clear enough.
The instantaneous ordinary chirpyness (symbol c) is a normalized version, defined as the rate of change of the instantaneous frequency: [3] = = Ordinary chirpyness has units of square reciprocal seconds (s −2); thus, it is analogous to rotational acceleration.
Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing.
The instantaneous amplitude, and the instantaneous phase and frequency are in some applications used to measure and detect local features of the signal. Another application of the analytic representation of a signal relates to demodulation of modulated signals .
The instantaneous frequency of a VCO is often modeled as a linear relationship with its instantaneous control voltage. The output phase of the oscillator is the integral of the instantaneous frequency.
The resulting frequency spectrum shows the frequency content of the signal. From the frequency spectrum, it is possible to identify the dominant frequency components, which correspond to the various orders of the rotating machinery. Once the orders are identified, a tracking algorithm is used to track the frequency variations of each order over ...