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Statements

Subject Item
dbr:Instantaneous_phase_and_frequency
rdfs:label
瞬時頻率 Instantaneous phase and frequency
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 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).
foaf:depiction
n8:Instantaneous_(wrapped)_phase;_one_360°_plot_stacked_3_times_vertically.jpg n8:Phase_vs_Time,_wrapped_and_unwrapped.jpg
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dbc:Signal_processing dbc:Digital_signal_processing dbc:Fourier_analysis dbc:Time–frequency_analysis dbc:Electrical_engineering dbc:Audio_engineering
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n8:Phase_vs_Time,_wrapped_and_unwrapped.jpg?width=300
dbo: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. 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
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wikipedia-en:Instantaneous_phase_and_frequency