This paper shows that members of the fourier transform family are the only linear transforms that have a convolution theorem, that is, that can replace O(N 2) operations of a convolution in a time domain by O(N) operations in a transform domain. Generally, there is an additional cost to compute the transform itself. Our observation is motivated by recent activity in wavelet and subband decompos...

An example of application of the wavelet transform to electrocardiography is described in the paper. The transform is exploited as a first stage of an ECG signal compression algorithm. The signal is decomposed into particular timefrequency components. Some of the components are removed because of their low influence to signal shape due to nonstationary character of ECG. Resulted components are ...

The Burrows-Wheeler Transform (bwt) produces a permutation of a string X, denoted X∗, by sorting the n cyclic rotations of X into full lexicographical order, and taking the last column of the resulting n× n matrix to be X∗. The transformation is reversible in O(n) time. In this paper, we consider an alteration to the process, called k-bwt, where rotations are only sorted to a depth k. We propos...

An arithmetical function f is said to be even (mod r) if f (n) = f ((n, r)) for all n ∈ Z + , where (n, r) is the greatest common divisor of n and r. We adopt a linear algebraic approach to show that the Discrete Fourier Transform of an even function (mod r) can be written in terms of Ramanujan's sum and may thus be referred to as the Discrete Ramanujan-Fourier Transform.

Combined use of the X-ray (Radon) transform and the wavelet transform has proved to be useful in application areas such as diagnostic medicine and seismology. In the present paper, the wavelet X-ray transform is introduced. This transform performs one-dimensional wavelet transforms along lines in R n , which are parameterized in the same fashion as for the X-ray transform. It is shown that the ...

We develop parallel algorithms to compute the Hough transform on a reconfigurable mesh with buses (RMESH) multiprocessor. The p angle Hough transform of an N×N image can be computed in O (plog(N/p)) time by an N×N RMESH, in O ((p/N)logN) time by an N×N 2 RMESH with N copies of the image pretiled, in O ((p/√ N )logN) time by an N 1.5×N 1.5 RMESH, and in O ((p /N)logN) time by an N 2×N 2 RMESH.

In this paper, a relation for finding type-II discrete sine transform (DST) from type-I discrete Hartley transform (DHT) has been derived. The transform length N is taken as even. Using this relation, the (N 1) output components of DST can be realized from DHT. The DHT is one of the transforms used for converting data in time domain into frequency domain using only real values.

Sampling rate conversion (SRC) is one of important issues in modern sampling theory. It can be realized by up-sampling, filtering, and down-sampling operations, which need large complexity. Although some efficient algorithms have been presented to do the sampling rate conversion, they all need to compute the N-point original signal to obtain the up-sampling or the down-sampling signal in the tim...

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...

Abstract. Computing the Fourier transform of a function in polar coordinates is an important building block in many scientific disciplines and numerical schemes. In this paper we present the pseudo-polar Fourier transform that samples the Fourier transform on the pseudo-polar grid, also known as the concentric squares grid. The pseudo-polar grid consists of equally spaced samples along rays, wh...