ANATRANS Analytic part of signal. XP=ANATRANS(X) returns the analytic part of the real-valued signal X, which is a column vector or a matrix with 'time' in columns. XP is defined for real X such that X = REAL(XP) = 1/2*(XP+CONJ(XP)). ANATRANS removes the mean of the signal. It does not detrend, so if your time series has a linear trend you may wish to call DETREND first. [XP1,XP2,...,XPM]=ANATRANS(X1,X2,...,XM) also works for multiple input arguments. ANATRANS(X,DIM) optionally applies the analytic transform along dimension DIM, instead of along the first dimension. ___________________________________________________________________ Complex-valued signals [ZP,ZN]=ANATRANS(Z,CONJ(Z)) returns the analytic part ZP of the complex-valued signal Z, and the analytic part ZN of its conjugate. The normalization for complex-valued signals differs from that for real valued signals. ZP and ZN are defined such that Z=ZP+CONJ(ZN). The analytic part of a real-valued signal and that of a complex-valued signal are thus defined differently by a factor of two, following the convention of Lilly and Gascard (2006) and Lilly and Olhede (2010). Note that the equality Z=ZP+CONJ(ZN) is not necessarily exact, due to issues relating to boundary effects from the time series edges. ___________________________________________________________________ Boundary conditions ANATRANS(...,STR), where STR is a string, optionally specifies the boundary condition to be imposed at the edges of the time series. Valid options for STR are STR = 'periodic' for periodic boundary conditions STR = 'zeros' for zero-padding beyond the endpoints STR = 'mirror' for reflecting the time series at both ends The default value of STR is 'mirror', as this tends to minimize the `edge effects' that occur near the ends of the time series. ___________________________________________________________________ Returning frequency domain version ANATRANS(...,'frequency') suppresses a final inverse Fourier transform, so that output fields will be analytic signals in the frequency domain. This is mainly useful for calculation of frequency-domain moments, as in FREQMOM, for large datasets where optimization is a priority. The 'frequency' flag implies a 'periodic' boundary condition, so a separate boundary condition flag cannot be used in this case. ___________________________________________________________________ 'anatrans --t' runs some tests. Usage: z=anatrans(x); z=anatrans(x,dim); z=anatrans(x,dim,'periodic'); [zp,zn]=anatrans(z,conj(z)); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2004--2019 J.M. Lilly --- type 'help jlab_license' for details