The Truncated Fourier Transform (tft) is a variation of the Discrete Fourier Transform (dft/fft) that allows for input vectors that do not have length 2 n for n a positive integer. We present the univariate version of the tft, originally due to Joris van der Hoeven, heavily illustrating the presentation in order to make these methods accessible to a broader audience.

We test various features for recognition of leaves of wooden species. We compare Fourier descriptors, Zernike moments, Legendre moments and Chebyshev moments. All the features are computed from the leaf boundary only. Experimental evaluation on real data indicates that Fourier descriptors slightly outperform the other tested features.

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...

We give a new generalization for Haar functions. The generalization starts from the Walsh-like functions and based on the connection between the original Walsh and Haar systems. We generalize the Haar– Fourier Transform too.

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of...