About: Instantaneous phase and frequency

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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 change 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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rdfs:label	Instantaneous phase and frequency (en) 瞬時頻率 (zh)
rdfs:comment	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 change 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)
foaf:depiction
dcterms:subject	Fourier analysis Audio engineering Signal processing Time–frequency analysis Digital signal processing Electrical engineering
Wikipage page ID	3125808 (xsd:integer)
Wikipage revision ID	1102902748 (xsd:integer)
Link from a Wikipage to another Wikipage	Fourier analysis Argument (complex analysis) Complex number Analytic signal Signal processing Principal value Audio engineering Signal processing Time–frequency analysis Digital signal processing Dirac delta Hilbert transform Electrical engineering Frequency modulation Temporal rate of change Negative frequency Group delay Instantaneous amplitude
sameAs	Instantaneous phase and frequency Instantaneous phase and frequency Instantaneous phase and frequency
dbp:wikiPageUsesTemplate	dbt:Open-closed dbt:Cite_book dbt:Pi dbt:Reflist dbt:Short_description dbt:Technical dbt:Closed-open
thumbnail	wiki-commons:Special:FilePath/Phase_vs_Time,_wrapped_and_unwrapped.jpg?width=300
has abstract	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 change 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)
prov:wasDerivedFrom	wikipedia-en:Instantaneous_phase_and_frequency?oldid=1102902748&ns=0
page length (characters) of wiki page	8994 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Instantaneous_phase_and_frequency
is Link from a Wikipage to another Wikipage of	Instantaneous phase Speech processing Analog television Instantaneous frequency Unwrapped phase Wrapped phase Phase unwrapping Phase wrapping Instantaneous angular frequency Instantaneous ordinary frequency
is Wikipage redirect of	Instantaneous phase Instantaneous frequency Unwrapped phase Wrapped phase Phase unwrapping Phase wrapping Instantaneous angular frequency Instantaneous ordinary frequency
is foaf:primaryTopic of	wikipedia-en:Instantaneous_phase_and_frequency

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