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get_ofac_hifac.m
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get_ofac_hifac.m
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function [ofac, hifac] = get_ofac_hifac( elevAngles, cf, maxH, desiredPrecision)
% function [ofac, hifac] = get_ofac_hifac(elevAngles,cf,maxH,desiredPrecision)
%
% Authors: Kristine M. Larson and Carolyn Roesler, March 10, 2018
%
% This function computes two factors - ofac and hifac - that are inputs to the
% Lomb-Scargle Periodogram code lomb.m. The ofac (oversampling factor) and
% hifac (high frequency factor) define the LSP frequency grid spacing
% and maximum frequency.
% We follow the terminology and discussion from Press et al. (1992)
% in their LSP algorithm description.
%----------------------------------------------------------------------------
% INPUT
% elevAngles: vector of satellite elevation angles in degrees
% cf: (L-band wavelength/2 ) in meters
% maxH: maximum LSP grid frequency in meters
% i.e. how far you want the reflector height to be estimated
% desiredPrecision: the LSP frequency grid spacing in meters
% i.e. how precise you want he LSP reflector height
% to be estimated
% ---------------------------------------------------------------------------
% OUPUT
% ofac: oversampling factor
% hifac: high-frequency factor
%----------------------------------------------------------------------------
%
% For the GNSS_-IR application, we can write: SNR = A.cos( 2.pi.H.X)
% The SNR data points are sampled with the variable
% X= ( 2.sin(elevAngles)/ wavelength ), in units of inverse meters
% so that their spectral content H is expressed in meters.
%
%
% The oversampling factor (ofac) defines the grid spacing between the
% frequencies H in order to find the top of the spectral peak to
% a desired precision.
% For N data observed during a rectangular window of length:
% W = Xmax - Xmin
% the frequency peaks have a characteristic width 1/W and we oversample
% each peak by (ofac) using a grid spacing of 1/(ofac.W) (in meters)
%
% NB: don't be surprised if (ofac) is much larger than the typical
% 4-10 given in the literature.
%
% The (hifac) factor defines the frequency grid maximum frequency Hmax,
% relative to the averaged-Nyquist frequency (fc) i.e. the Nyquist
% frequency if all the N data samples were evenly spaced over the
% span W of the observing window :
% fc = N/(2*W) and hifac = maxH/fc;
%
% NB: don't be surprised if (hifac) is much less than the typical
% 5 >= given in the literature
%
% NB: (fc) is only a reference frequency. For non-uniformly sampled data this
% averaged-Nyquist frequency (fc) may have nothing to do with the real
% pseudo- Nyquist or Nyquist-like frequency limit that exists in the data
% ( see VanderPlas, 2017)
%-------------------------------------------------------------------------------
% SNR expressed as a function of X
X= sind(elevAngles)/cf; % in units of inverse meters
% number of observations
N = length( X);
% observing Window length (or span)
W = max(X) - min(X); % units of inverse meters
% characteristic peak width
characteristic_peak_width= 1/W; % in meters
% oversampling factor
ofac = characteristic_peak_width/desiredPrecision;
% Nyquist frequency if the N observed data samples were evenly spaced
% over the observing window span W
fc = N/(2*W); % in meters
% The high-frequency factor is defined relative to fc
hifac = maxH/fc;