A Generalized Approach to Linear Transform Approximations with Applications to the Discrete Cosine Transform

A Generalized Approach to Linear Transform Approximations with Applications to the Discrete Cosine Transform

This paper aims to develop a generalized framework to systematically trade off computational complexity with output distortion in linear transforms such as the DCT, in an optimal manner. The problem is important in real-time systems where the computational resources available are time-dependent. Our approach is generic and applies to any linear transform and we use the DCT as a specific example...

JPEG Encoder using Discrete Cosine Transform & Inverse Discrete Cosine Transform

In the past decade, the advancement in data communications was significant during explosive growth of the Internet, which led to the demand for using multimedia in portable devices. Video and Audio data streams require a huge amount of bandwidth to be transferred in an uncompressed form. The objective of this paper is to minimize the number of bits required to represent an image and also the ac...

The Discrete Cosine Transform

Each Discrete Cosine Transform uses N real basis vectors whose components are cosines. In the DCT-4, for example, the jth component of v k is cos(j + 1 2)(k + 1 2) N. These basis vectors are orthogonal and the transform is extremely useful in image processing. If the vector x gives the intensities along a row of pixels, its cosine series P c k v k has the coeecients c k = (x; v k)=N. They are q...

Discrete Cosine Transform

On discrete cosine transform

The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new...