%** create plots of power specra for paleoclimate data sets
%   with UNIFORM sample interval
%
%   this script uses quick and easy function f_powerspec 
%   [freq, pow]=f_powerspec(SDATA, SF)
%           
%   SDATA:  equally-spaced (in time) samples         
%   SF:     sample frequency
%   freq:   frequency spectrum
%   pow:    signal power at those frequencies
%
%   this script uses function f_autorcorr
%   R=f_autorcorr(SDATA, SF)
%
%   R:      level of correlation at a range of lags 
%           1: lag in time units
%           2: correlation
%
%  detrend the data to clean up the analysis
%  buit-in Matlab detrend takes flags 'constant' and 'linear'


%* select time series
ts=detrend(T_akureyri(2:128,2),'linear');  % dependent variable
tst=T_akureyri(2:128,1);                    % independent variable (time)
sf=tst(2)-tst(1);

ttl='Akureyri January temperature';
fn=100;     % figure number


%* compute correlation and plot the result
autoC=f_autocorr(ts,sf);
[fSPAC, pSPAC]=f_powerspec(autoC(:,2), sf);

figure(fn)
subplot(3,1,1)
plot(tst,ts, '.m-')
ylabel('data');
xlabel('time')
title(ttl)

subplot(3,1,2)
plot(autoC(:,1), autoC(:,2), 'm-')
grid on
ylabel('correlation'), xlabel('lag')

subplot(3,1,3)
plot(fSPAC(2:length(fSPAC)), pSPAC(2:length(fSPAC)))
grid on
ylabel('power')
xlabel('frequency spectrum of autocorrelation (cycles/a)')