BLURSPEC Returns the blurred and aliased spectrum given the autocovariance. BLURSPEC is used to rapidly compute blurred, aliased, and other modified versions of a spectrum from a known autocovariance. Performing these calculations in the time domain, making use of Fourier relationships between modified versions of the autocovariance and spectrum, is much faster than working in the frequency domain. __________________________________________________________________ Blurred and aliased spectra [F,S]=BLURSPEC(R) inverse Fourier transforms a given *one-sided* autocovariance R to obtain a spectrum S that incorporates the effects of aliasing, as well as blurring by the default taper, the 'boxcar'. Here F is an array of frequencies and S is the one-sided Fourier spectrum. If R is length N, the output arrays will be length (N/2+1) if N is even and (N+1)/2 if N is odd. [F,SPP,SNN]=BLURSPEC(R) for complex-valued R returns SPP and SNN, the positive and negative rotary spectra, respectively. BLURSPEC(DT,R) optionally uses the sample interval DT in computing the frequency array F, and in setting the spectral levels. __________________________________________________________________ Tapered and aliased spectra BLURSPEC(R,'tapered',TAPER) incorporates the spectral smoothing due to the use of data TAPER, rather than the boxcar taper, in addition to the effects of aliasing. TAPER must be the same length as R. Note that BLURSPEC(R,'tapered',[]) simply returns the blurred spectrum, as an empty taper is taken to indicate the periodogram. BLURSPEC(R,'window',WIN) uses the pre-computed window that is to multiply the autocovariance function WIN. This is the half of the sequence obtained by convolving the taper with itself. This version is primarily used for speed in an internal call from MATERNFIT. __________________________________________________________________ Aliased-only spectrum BLURSPEC(R,'aliased') computes an approximation to *aliased* spectrum, without blurring. This approximation will be accurate to the extent that R has decayed to zero by the end of its duration. This is much faster than explicitly summing over aliased frequencies. __________________________________________________________________ Differenced spectra BLURSPEC(R,'difference') returns the blurred and aliased spectrum of the first forward difference of the process with autocovariance R. In this case the output will be length N-1. BLURSPEC(R,'seconddifference') returns the blurred and aliases spectrum of the second forward difference of the process with autocovariance R. The output will be length N-2. These options can be combined with the 'taper' and 'aliased' options described above. __________________________________________________________________ 'blurspec --t' runs some tests. Usage: [f,S]=blurspec(R); [f,Spp,Snn]=blurspec(dt,R); [f,Spp,Snn]=blurspec(dt,R,'tapered',TAPER); [f,Spp,Snn]=blurspec(dt,R,'aliased'); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2015--2020 J.M. Lilly and A.M. Sykulski --- type 'help jlab_license' for details