The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...

This paper proposes new image compression technique that uses Real Fourier Transform. Discrete Fourier Transform (DFT) contains complex exponentials. It contains both cosine and sine functions. It gives complex values in the output of Fourier Transform. To avoid these complex values in the output, complex terms in Fourier Transform are eliminated. This can be done by using coefficients of Discr...

This paper presents a study of the Modified Discrete Cosine Transform (MDCT) and its implications for audio coding and error concealment from the perspective of Fourier frequency analysis. A relationship between the MDCT and DFT via Shifted Discrete Fourier Transform (SDFT) is established, which provides a possible fast implementation of MDCT employing an FFT routine. The concept of Time Domain...

Digital image watermarking is the insertion of watermarks into digital media. Several types methods used are Discrete Cosine Transform (DCT) and Fourier (DFT). Both these work in frequency domain (transform). using carried out on coefficient. This study 30 data as material for watermaking analysis with 10 each binary, grayscale color images jpg, png bmp formats. binary domains conversions from ...

We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT), respectively. As a consequence, important variants such as warped DFT, DCT, DST also can be view...

Let GH(n; G) denote a generalised Hadamard matrix of order n over the group G, and let EA( q) denote the elementary abelian group of prime power order q. We use a computer to investigate the applicability of a recently discovered general construction for GH (4tq; E A( q)) in the case t = 2. In particular, we prove that G H (8p; Zp) exist for all primes p > 19, and obtain GH(8q; EA(q)) for all p...

This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relat...