MORSESPACE is the jWavelet module of jLab.

 MORSESPACE  Logarithmically-spaced frequencies for generalized Morse wavelets.
 
    F=MORSESPACE(GAMMA,BETA,N) generates a frequency array for the 
    generalized Morse wavelet transform of an N-point time series. The 
    wavelets are specified by GAMMA and BETA.  
 
    LOG(F) is uniformly spaced, following convention for wavelet analysis.
 
    F has units of *radians* per sample point, and is a column vector with 
    the frequencies arranged in decending order. 
    
    In this usage, the frequencies F are determined using default settings,
    described below, which should be appropriate for most applications.  
 
    Additional control over the frequency array F can be obtained using the
    following alternate usages.
 
    For details on this calculation, see Lilly (2016).
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    High- and low-frequency specification
 
    F=MORSESPACE(GAMMA,BETA,HIGH,LOW) explicitly sets the high-frequency
    and low-frequency cutoffs for the frequency array.  
 
    The first (largest) value of F is then just smaller than HIGH and the 
    smallest is just larger than LOW.
 
    HIGH and LOW have units of *radian* per unit sample point.
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    High-frequency cutoff
 
    The highest frequency can be set to be the minimum of a specified value
    and a cutoff frequency based on a Nyquist overlap condition.
 
    F=MORSESPACE(GAMMA,BETA,{ETA,HIGH},LOW) sets the highest frequency 
    to be the minimum of the specified value HIGH, and the largest 
    frequency for which the wavelet will satisfy the threshold level ETA. 
 
    Here ETA be a number between zero and one specifying the ratio of a
    frequency-domain wavelet at the Nyquist frequency to its peak value.
 
    Note that in this usage, {ETA,HIGH} is a cell array with two entries.
 
    The simplified usage F=MORSESPACE(GAMMA,BETA,N) corresponds to the 
    choice ETA=0.1, so that by default, the highest-frequency wavelet 
    will decay to at least 10% of its peak value at the Nyquist frequency.
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    Low-frequency cutoff
 
    The lowest frequency can be set to a cutoff frequency based on an 
    endpoint overlap condition.
 
    F=MORSESPACE(GAMMA,BETA,HIGH,{P,N}) sets the lowest frequency such that
    the lowest-frequency wavelet will reach some number P times its central 
    window width at the ends of the time series. 
   
    P is called the packing number.  A choice of P=1 corresponds to 
    roughly 95% of the time-domain wavelet energy being contained within 
    the time series endpoints for a wavelet at the center of the domain.
 
    F=MORSESPACE(GAMMA,BETA,HIGH,{P,N,LOW}) alternately chooses the maximum 
    of the R-level cutoff frequency, and a specified low frequency LOW.
    
    The simplified usage F=MORSESPACE(GAMMA,BETA,N) corresponds to the
    default value P=5.  At the lowest frequency, five wavelets will then
    fit into the time series, with 5% energy overlap between them.
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    Wavelet density
 
    F=MORSESPACE(GAMMA,BETA,HIGH,LOW,D) controls the number of points in 
    the frequency array through the 'density' D. 
 
    Higher values of D mean more overlap in the frequency domain. The
    default value of the density is D=4.
 
    When D=1, the peak of one wavelet is located at the half-power points 
    of the adjacent wavelet. D=4 means that four other wavelets will occur 
    between the peak of one wavelet and its half-power point. 
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    See also MORSEWAVE, WAVETRANS.
   
    Usage: f=morsespace(ga,be,N);
           f=morsespace(ga,be,high,low,D);
           f=morsespace(ga,be,{eta,high},low,D);
           f=morsespace(ga,be,{eta,high},{p,N},D);
           f=morsespace(ga,be,{eta,high},{p,N,low},D);
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2009--2016 J.M. Lilly --- type 'help jlab_license' for details

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