Harmonic analysis of time series

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:

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