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Harmonic analysis of time series

Asked by edward kabanyas on 8 Sep 2019
Hi all,
I want to make harmonic analysis for my time series data to see first (diurnal) and second harmonic (semi diurnal variation). I simply tried the following code:
xxx = 0:1:23;
asc = Hour';
dec = xxx';
%FFT
d = fft(dec);
m = length(dec);
M = 3;
a0 = d(1)/m;
an = 2*real(d(2:M))/m;
bn = -2*imag(d(2:M))/m;
n = 1:length(an);
y1 = a0 + 0*cos(2*pi*1*x/23)+0*sin(2*pi*1*x/23);
y2 = a0 + an(1)*cos(2*pi*n(1)*x/23)+bn(1)*sin(2*pi*n(1)*x/23);
y3 = a0 + an(2)*cos(2*pi*n(2)*x/23)+bn(2)*sin(2*pi*n(2)*x/23);
y4 = a0 + an*cos(2*pi*n'*x/23) ...
+ bn*sin(2*pi*n'*x/23);
It seems ok, howewer in Statistical Methods in the Atmospheric Sciences book, the author use another method:
harmonic_equ.png
I want to make harmonic analysis using this equation and compare with the above code. Are there any body having experience with this question in Matlab?
Thank you for sharing.
Edward

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