The terms Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) are used to denote efficient and fast algorithms to compute the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT) respectively. The FFT/IFFT is widely used in many digital signal processing applications and the efficient implementation of the FFT/IFFT is a topic of continuous research.

We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been use...

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the underlying graph data domain. In this paper, we generalize one of the most important signal processing tools windowed Fourier analysis to the...

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...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

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...