Source: Signal Processing Stack Exchange

<>

Understanding Instantaneous Frequency

Definition and Concept

Instantaneous frequency is a concept used to describe non-monochromatic signals, defined as the temporal derivative of the oscillation phase. Unlike Fourier frequency, instantaneous frequency varies with time. For sinusoidal signals, the instantaneous frequency equals the oscillation frequency.

Applications

Instantaneous frequency is crucial in analyzing frequency noise, phase noise, and chirped optical pulses. In music, it is akin to specifying notes based on time intervals with specific instantaneous frequencies. However, for complex signals like white noise, the concept may pose challenges.

Instantaneous Frequency in Lasers

For single-frequency lasers, defining instantaneous frequency is straightforward. In multimode lasers, separating frequency components is necessary before determining their instantaneous frequencies. In chirped optical pulses, the instantaneous frequency changes throughout the pulse duration.

Relation to Fourier Frequency

The Fourier spectrum of a signal does not represent the probability distribution of instantaneous frequencies. The relationship between instantaneous frequency and Fourier frequency is intricate and not simply an r.m.s. value.

Measuring Instantaneous Frequency

Measuring the instantaneous frequency of an electronic signal can be done using a phase-locked loop with a voltage-controlled oscillator. Software phase trackers and fast Fourier transforms are alternative techniques for measuring instantaneous frequency.

Conclusion

Understanding instantaneous frequency is essential for analyzing non-monochromatic signals and is particularly valuable in fields like optics and music. While it has practical applications, the relationship between instantaneous frequency and Fourier frequency requires careful consideration.

Source: Signal Processing Stack Exchange
Feel free to comment your thoughts.