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.

From the main equation (ax2 + bx + c)y′′ n (x) + (dx + e)y′ n(x)− n((n− 1)a+ d)yn(x) = 0, n∈ Z+, six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x = pz−1 + q, p = 0, q ∈ R. Some new int...

We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of ǫ, t...

The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N . In this paper, we propose a fast a...

A new branch of Hough Transform algorithms, called probabilistic Hough Transforms, has been actively developed in recent years. One of the rst was a new and eecient probabilistic version of the Hough Transform for curve detection, the Randomized Hough Transform (RHT). The RHT picks n pixels from an edge image by random sampling to solve n parameters of a curve and then accumulates only one cell...

Given an n×n binary image I of white and black pixels, we present a simple algorithm for computing the distance transform and the nearest feature transform using the Euclidean metric. The running time of the algorithm is linear in the input size.

A new and eecient version of the Hough Transform for curve detection, the Randomized Hough Transform (RHT), has been recently suggested. The RHT selects n pixels from an edge image by random sampling to solve n parameters of a curve and then accumulates only one cell in a parameter space. In this paper, the RHT is related to other recent developments of the Hough Transform by experimental tests...

Fourier transform is among the most widely used tools in computer science. Computing the Fourier transform of a signal of length N may be done in time Θ(N logN) using the Fast Fourier Transform (FFT) algorithm. This time bound clearly cannot be improved below Θ(N), because the output itself is of length N . Nonetheless, it turns out that in many applications it suffices to find only the signifi...

Compression of 2 dimensional data is important for the efficient transmission, storage and manipulation of Images. The most common technique used for lossy image compression relies on fast application of the Discrete Cosine Transform (DCT). The cosine transform has been heavily researched and many efficient methods have been determined and successfully applied in practice; this paper presents a...

We give the upper and lower bounds of the Möbius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of n elements. We find that the absolute value of the bounds tend to 4 n/2 √ πn/2 when n is large. We establish also the bounds of the interaction transform and Banzhaf interaction transform, as well as the bounds of the Möbius inverse for the subfamil...