Discrete cosine transform

Take an image of size MxM Consider the image in DCT domain, where the Discrete Cosine Transform has been done using block size N/N. There is a secret key K and a secret watermarking signal w. The watermarking signal w = [nq,..., wt is t = bits binary pattern. 

Time domain aliasing cancellation based filter banks. The Modified Discrete Cosine Transform (MDCT) was first proposed in [Princen et al., 1987] as a sub-band/transform coding scheme using Time Domain Aliasing Cancellation (TDAC). It can be viewed as a dual to the QMF-approach doing frequency domain aliasing cancellation. The window is constructed in a way that satisfies the perfect reconstruction condition ... 

Frequency Analysis. The Discrete Fourier Transform (and its fast implementation, the Fast Fourier Transform [Brigham, 1974]) (FFT) as well as its cousin, the Discrete Cosine Transform [Rao and Yip, 1990] (DCT) require block operations, as opposed to single sample inputs. The DFT can be described recursively, with the basis being the 2 point DFT calculated as follows ... 

Filterbank. A modified discrete cosine transform (MDCT/IMDCT) is used for the filter bank tool. The MDCT output consists of 1024 or 128 frequency lines. The window shape is selected between two alternative window shapes. 

Methods developed for traditional lossy image compression can be used in the compression of multispectral images. The discrete cosine transform (DCT),... 

DCT DIC DICOM DIM DWT Discrete Cosine Transformation Differential Interference Contrast Digital Imaging Communications in Medicine Diffraction Imaging Microscopy Discrete Wavelet Transform... 

Keywords Cryptanalysis, Digital Watermarking, Discrete Cosine Transform, Subset Sum. 

The invertible transformation stage uses a different mathematical basis of features in an attempt to decorrelate the data. The resulting data will have a set of features that capture most of the independent features in the original data set. Typical features used include frequency and spatial location. The transformation is nearly loss-less as it is implemented using real arithmetic and is subject to (small) truncation errors. Examples of invertible transforms include the discrete cosine transform (DCT), the discrete wavelet transform (DWT) and the wavelet packet transform (WPT). We will investigate these transforms later. 

A very popular representation in speech recognition is the mel-frequency cepstral coefficient or MFCC. This is one of the few popular represenations lhat does not use linear prediction. This is formed by first performing a DFT on a frame of speech, then performing a filter bank analysis (see Section 12.2) in which the frequency bin locations are defined to lie on the mel-scale. This is set up to give say 20-30 coefficients. These are then transformed to the cepstral domain by the discrete cosine transform (we use this rather than the DFT as we only require the real part to be calculated) ... 

Before a frame is quantized, it is desirable to eliminate redundant data in the frame. There are many techniques for reducing the spatial redundancy, but by far, DPCM and discrete cosine transformation-(DCT-) based coding are the most widely used techniques for intraframe compression. (Rabbani and Jones (1991) discuss many image compression techniques. See Further Information.)... 

Discrete cosine transformation (DCT) Decorrelates image data efficiently [Rao and Yip 1990]. 

Discrete cosine transform A mathematical transform that can be perfectly undone and which is useful in image compression. 

In the following sections a polymer-polymer-solvent blend phase separation is investigated, with the respect to self-assembly on a heterogeneously functionalized substrate. The evolutionary mechanisms were studied by measuring the characteristic length, and the influence of different compositions was examined. The effects of a heterogeneously functionalized substrate were studied, and a discrete cosine transform spectral method was employed to solve the nonlinear partial differential equation. A semi-implidt method was used in the time evolution this method was found to be efficient and unconditionally stable over large time steps [40] (see Section 15.1.4). 

The evolution of polymer composition in the spatial domain can be derived using the Cahn-Hilliard equation. In numerical simulations, the fourth-order nonlinear parabolic partial differential equations are solved using Fourier-spectral methods, while the partial differential equations are transferred by the discrete cosine transform into ordinary partial equations. The result is then transformed back with the inverse cosine transform to the ordinary space. 

The MFCC can then be derived by taking the log of the band-passed frequency response and calculating the Discrete Cosine Transform (DCT) for each intermediate signal. 

RM88] V. Rampa and G. De Micheli. Computer-aided synthesis of a Bi-dimensional discrete cosine transform chip. CSL Technical Report CSL-TR-88-363, Stanford, August 1988. 

---