Morlet wavelet
A commonly used complex-valued wavelet formed from a complex exponential function modulated by a Gaussian window. It has a one-sided (analytic) spectrum and provides both amplitude and phase information, and is widely applied in time-frequency analysis.
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The Morlet wavelet, as a representative complex wavelet, has a frequency-domain response that exists only on the positive-frequency side, its phase and amplitude information is fully preserved, and no cross-term interference is introduced in energy computation, so the scalogram exhibits a smooth envelope.
Complex wavelets (such as Morlet and dual-tree complex wavelets) provide approximate shift invariance, and their phase information can be used for precise instantaneous frequency and phase analysis.
The traditional discrete wavelet transform (DWT) lacks shift invariance due to downsampling, causing coefficients to oscillate with shifts; complex wavelets (such as the Morlet continuous transform and DT-CWT) introduce redundancy through oversampling or the dual-tree structure, thereby obtaining approximate shift invariance.
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The Morlet wavelet, as a representative complex wavelet, has a frequency-domain response that exists only on the positive-frequency side, its phase and amplitude information is fully preserved, and no cross-term interference is introduced in energy computation, so the scalogram exhibits a smooth envelope.
50%UnverifiedComplex wavelets (such as Morlet and dual-tree complex wavelets) provide approximate shift invariance, and their phase information can be used for precise instantaneous frequency and phase analysis.
50%UnverifiedThe traditional discrete wavelet transform (DWT) lacks shift invariance due to downsampling, causing coefficients to oscillate with shifts; complex wavelets (such as the Morlet continuous transform and DT-CWT) introduce redundancy through oversampling or the dual-tree structure, thereby obtaining approximate shift invariance.
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