This is a snapshot from some text I'm currently reading which aims to describe how the amplitude and phase of a seasonal cycle can be determined:
I think I understand the text but I'm unsure when they refer to 'using the Fourier transform'. Does the equation that follows that comment qualify as a Fourier transform? On first reading I thought that this meant that X was the complex array returned by fft, but according to the description, this doesn't seem to be the case.
I have written this up in matlab as:
datev = datevec(dates); uyear = unique(datev(:,1)); % this is the unique years of data t = 0.5:1:11.5; t = t'; for j = 1:length(uyear); x = yt(datev(:,1) == uyear(j)); yx(j,:) = exp(2.*pi.*1i*t/12).*x; end Yx = 2/12.*sum(yx,2); Amp = abs(Yx); phase = angle(Yx);
According to the text does this make sense? Also, how can this be described as a Fourier transform?