Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Implementation and performance of the fast Hartley transform

Abstract: The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware. They describe the modifications required to convert existing fast Fourier transform (FFT) programs to execute FHTs, showing the ease with which these modifications can be implemented. They compare execution time and memory storage requirements of both transforms and present power spectrum calculation and convolution as illustrative examples to compare the performances of the two transform techniques. They also give a comparative survey of the performances of various microprocessors and digital signal processors in FFT and FHT computation. >

Multirate-Based Fast Parallel Algorithms for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Abstract: Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.

On the range of the Fourier transform connected with Riemann-Liouville operator

Abstract: We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator ℛ α , α ≥ 0 and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.

A new technique for velocity estimation of large moving objects

Abstract: A technique for motion estimation of large moving objects is presented. This technique is based on analyzing the Hartley transform spectrum of the image sequence directly, instead of using it to compute other transforms. In this technique, the fast Hartley transform (FHT) is applied to the image sequence and followed by a peak detection procedure. The location of the peak is related to the velocity of the moving object. Dividing the temporal frequency (f/sub p/) corresponding to the detected peak by the corresponding spatial frequency (k/sub p/) gives the velocity of the moving object. The Fourier spectrum for a spatial frequency of k/sub p/ is then computed. This is followed by a peak detection of the Fourier spectrum to validate the previous results and find the direction of the velocity of the moving object. This method is faster than other techniques based on the Fourier transform. >