In this paper, it is shown that the use of real trigonometric transforms can advantageously replace the Fourier transform in optical communication systems, for both all-optical and electronic signal processing. All-optical discrete Hartley transform (DHT) and discrete Cosine transform (DCT) architectures for high-speed optical signal processing, filtering and data compression are given and comp...

In this report we analyse the image reconstruction accuracy when using different orthogonal basis functions as the kernel for a reversible image transform. In particular we examine the Discrete Cosine Transform(DCT), Discrete Tchebichef Transform(DTT), Haar Transform, and Walsh-Hadamard Transforms(WHT). We have found that the DCT provides the greatest energy compactness properties for continuou...

Recent results by Van Buskirk et al. have broken the record set by Yavne in 1968 for the lowest arithmetic complexity (exact count of real additions and multiplications) to compute a power-of-two discrete Fourier transform. Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the co...

The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFTs of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (...

It is well-known that the discrete Fourier transform (DFT) can be characterized as decomposition matrix for the polynomial algebra C [x℄=(xn 1). This property gives deep insight into the DFT and can be used to explain and derive its fast algorithms. In this paper we present the polynomial algebras associated to the 16 discrete cosine and sine transforms. Then we derive important algorithms by m...

with the increase of communication and financial transaction through internet, on-line signature verification is an accepted biometric technology for access control and plays a significant role in authenticity and authorization in modernized society. therefore, fast and precise algorithms for the signature verification are very attractive. the goal of this paper is modeling of velocity signal t...

Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is interrelation between generalized cosine transforms of different kinds and their application to investigation of certai...

The growth of networked multimedia systems has complicated copyright enforcement relative to digital images. One way to protect the copyright of digital images is to add an invisible structure to the image (known as a digital watermark) to identify the owner. In particular, it is important for Internet and image database applications that as much of the watermark as possible remain in the image...

The problems of unified efficient computations of the discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), and their inverse transforms are considered. In particular, a new scheme employing the time-recursive approach to compute these transforms is presented. Using such approach, unified parallel lattice structures that can dually generate the DCT an...

The discrete wavelet transform (DWT) and filtering algorithms, together with certain classes of trigonometric transforms, are among the most frequently used methods in digital signal processing (DSP) applications. For example, the DWT is used in detection, identification, denoising, prediction, channel coding, and compression such as in the JPEG2000 standard. In many of these applications, filt...