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How to Estimate & Interpret the Instantaneous Frequency

There are many different types of electromagnetic radiation, which includes radio waves, microwaves and light. Electromagnetic waves consist of electric and magnetic fields that oscillate in perpendicular directions. The oscillatory motion can be described by a sinusoidal function (such as sine or cosine) with a set wavelength, frequency and phase. The instantaneous frequency is a measure of how the phase of a wave changes with time and can be calculated using a simple formula.

Things You'll Need

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Instructions

- 1
  Write down the mathematical form of the sinusoidal function. There are many different sinusoidal functions, but the most general take the form:
  
  g=g0.exp(i.w.t)
  
  Where g0 is the amplitude of the wave, i is the imaginary number, w is the angular frequency and t is the time.
- 2
  Write down the expression for the phase:
  
  p = s.ln(g)
  
  Where s is the magnitude of the phase, and g is the sinusoidal function.
- 3
  Calculate instantaneous frequency. The instantaneous frequency is equal to the rate of change of phase:
  
  f= dp/dt
  
  Substituting in the value of p leads to:
  
  s.d/dt (ln(g(t)) = (s/g)dg/dt
  
  Using this expression on the sinusoidal function leads to:
  
  g=g0.exp(i.w.t)
  
  f=(s/g)g0.i.w.exp(i.w.t.)
  
  The instantaneous frequency can be interpreted as how the phase of a wave varies with time.

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