## preprocessor Fast fourier transform for deasonalizing data in MATLAB?

detrended = dat - trend;

tim = (time - time0)/timestep; % <-- acquisition times for your *new* data, normalized NFpick = [2 7 13]; % <-- channels you picked to build the detrending baseline % Compute the trend mu = mean(ts); tsdft = fft(ts-mu); Nchannels = length(ts); % <-- size of time domain data Mpick = 2*length(NFpick); X(:,1:2:Mpick) = cos(2*pi*(NFpick-1)'/Nchannels*tim)'; X(:,2:2:Mpick) = sin(-2*pi*(NFpick-1)'/Nchannels*tim)'; % Generate beta vector "bet" containing scaled amplitudes from the spectrum bet = 2*tsdft(NFpick)/Nchannels; bet = reshape([real(bet) imag(bet)].', numel(bet)*2,1) trend = X*bet + mu;

(1) Perform a rough "detrending" by removing the DC component (the mean of the time-domain data)

(2) FFT and inspect the data, choose frequency channels that contain most of the signal.

In your case it seems you are interested in the residuals. The initial approach is therefore to proceed as in the example as follows:

The following code shows how you can do this:

To remove the trend just do

What you want to do is certainly possible, you are on the right track, but you seem to misunderstand a few points in the example. First, it is shown in the example that the technique is the equivalent of linear regression in the time domain, exploiting the FFT to perform in the frequency domain an operation with the same effect. Second, the trend that is removed is not linear, it is equal to a sum of sinusoids, which is why FFT is used to identify particular frequency components in a relatively tidy way.

You can then use those channels to generate a trend in the time domain and subtract that from the original data to obtain the residuals. You need not proceed by using IFFT, however. Instead you can explicitly sum over the cosine and sine components. You do this in a way similar to the last step of the example, which explains how to find the amplitudes via time-domain regression, but substituting the amplitudes obtained from the FFT.

where dat is your new data acquired at times tim. Make sure you define the time origin consistently. In addition this assumes the data is real (not complex), as in the example linked to. You'll have to examine the code to make it work for complex data.

## Discussion