*3.3. Action Representation*

In the next step, all *SD* vectors are transformed into action representations (*AR*) using the Discrete Fourier Transform. A *SD*, in its form, is similar to shape signature and the one-dimensional version of the Discrete Fourier Transform can be applied. The number of elements in each *SD* is different due to various number of frames in video sequences. Therefore, to prepare action representations equal in size, the *N*-point Discrete Fourier Transform is calculated, where *N* is the predefined number of resultant Fourier coefficients. If *N* is larger than *n*, then *SD* vectors are appended with zeros in the time domain (zero-padding) which corresponds to the interpolation in the frequency domain. Otherwise, *SD* vectors are truncated and then Fourier coefficients are calculated. As a result, each *AR* contains *N* absolute values of Fourier coefficients. Usually, it was recommended that the vectors under transformation should have a length equal to a power of 2, due to the computational complexity. However, current implementations of the Discrete Fourier Transform can handle arbitrary size transforms, e.g., Fast Fourier Transform algorithm available in the FFTW library [35].
