How to remove periodicity in hourly wind speed data by using fourier transform in matlab

Question

Review for removing periodicsI have a dataset that contains hourly wind speed data for 7 seven. I am trying to implement a forecasting model to the data and the review paper states that trimming of diurnal, weekly, monthly, and annual patterns in data significantly enhances estimation accuracy. They then follow along by using the fourier series to remove the periodic components as seen in the image. Any ideas on how i model this in matlab?

Answer 1

I am afraid this topic is not explained "urgently". What you need is a filter for the respective frequencies and a certain number of their harmonics. You can implement such a filter with an fft or directly with a IIR/FIR-formula.

FFT is faster than a IIR/FIR-implementation, but requires some care with respect to window function. Even if you do a "continuous" DFT, you will have a window function (like exponential or gaussian). The window function determines the bandwidth. The wider the window, the smaller the bandwidth. With an IIR/FIR-filter the bandwidth is encoded in the recursive parameters.

For suppressing single frequencies (like the 24hr weather signal) you need a notch-filter. This also requires you to specify a bandwidth, as you can see in the linked article. The smaller the bandwidth, the longer it will take (in time) until the filter has evolved to the frequency to suppress it. If you want the filter to recognize the amplitude of the 24hr-signal fast, then you need a wider bandwidth. But then however you are going to suppress also more frequencies slightly lower and slightly higher than 1/24hrs. It's a tradeoff.

If you also want to suppress several harmonics (like described in the paper) you have to combine several notch-filters in series. If you want to do it with FFT, you have to model the desired transfer function in the frequency space and since you can do this for all frequencies at once, so it's more efficient.

An easy but approximate way to get something similar to a notch-filter including all harmonics is with a Comb-filter. But it's an approximation, you have no control over the details of the transfer function. You could do that in Matlab by adding to the original a signal that is shifted by 12hrs. This is because a sinusoidal signal will cancel with one that is shifted by pi.

So you see, there's lots of possibilities for what you want.