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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. The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function: where arg is the complex argument function.The instantaneous frequency is the temporal rate of the instantaneous phase. And for a real-valued function s(t), it is determined from the function's analytic representation, sa(t): where represents the Hilbert transform of s(t).

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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. The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function: where arg is the complex argument function.The instantaneous frequency is the temporal rate of the instantaneous phase. And for a real-valued function s(t), it is determined from the function's analytic representation, sa(t): where represents the Hilbert transform of s(t). When φ(t) is constrained to its principal value, either the interval (−π, π] or [0, 2π), it is called wrapped phase. Otherwise it is called unwrapped phase, which is a continuous function of argument t, assuming sa(t) is a continuous function of t. Unless otherwise indicated, the continuous form should be inferred. (en)
  • 在信號處理中,觀察信號的瞬時頻率是很重要的課題。假設一实信號 可寫成指數信號的N項相加(有無穷多種表示法,以 小的為宜,即, 其中 為虚常數。則瞬時頻率(以頻率表示, k=1,...,N (zh)
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  • 在信號處理中,觀察信號的瞬時頻率是很重要的課題。假設一实信號 可寫成指數信號的N項相加(有無穷多種表示法,以 小的為宜,即, 其中 為虚常數。則瞬時頻率(以頻率表示, k=1,...,N (zh)
  • Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function: where arg is the complex argument function.The instantaneous frequency is the temporal rate of the instantaneous phase. And for a real-valued function s(t), it is determined from the function's analytic representation, sa(t): where represents the Hilbert transform of s(t). (en)
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  • Instantaneous phase and frequency (en)
  • 瞬時頻率 (zh)
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