The Fourier transform and its extensions have historically been the prime vehi-
cle for signal analysis and representation. Since the early 1970s, block transforms
with real basis functions, particularly the discrete cosine transform (DCT), have
been studied extensively for transform coding applications. The availability of
simple fast transform algorithms and good signal coding performance made the
DCT the standard signal decomposition technique, particularly for image and
video. The international standard image-video coding algorithms, i.e., CCITT...
The idea of a lapped transform (LT) maintaining orthogonality and non-expansion of the samples
was developed in the early 1980s at MIT by a group of researchers unhappy with the blocking artifacts
so commonin traditional block transformcoding of images.
EURASIP Journal on Applied Signal Processing 2003:12, 1210–1218 c 2003 Hindawi Publishing Corporation
Nonstationary Interference Excision in Time-Frequency Domain Using Adaptive Hierarchical Lapped Orthogonal Transform for Direct Sequence Spread Spectrum Communications
Department of Electronics Engineering, Shanghai Jiao Tong University, Shanghai 200030, China College of Information Engineering, Dalian Maritime University, Dalian, Liaoning 116026, China Email: firstname.lastname@example.org.
VNU Journal of Science, Mathematics - Physics 25 (2009) 21-38
Proper Orthogonal Decomposition and its Proper Transformations has been applied widely in many engineering topics including the wind engineering recently due to its advantage of optimum approximation of multi-variate random fields using the modal decomposition and limited number of dominantly orthogonal eigenvectors.
The idea of a lapped transform (LT) maintaining orthogonality and non-expansion of the samples was developed in the early 1980s at MIT by a group of researchers unhappy with the blocking artifacts so common in traditional block transform coding of images. The idea was to extend the basis function beyond the block boundaries, creating an overlap, in order to eliminate the blocking effect. This idea was not new, but the new ingredient to overlapping blocks would be the fact that
Power Spectral Density Analysis
In this chapter, general results for the power spectral density that facilitate evaluation of the power spectral density of speciﬁc random processes are given. First, the nature of the Fourier transform on the inﬁnite interval is discussed and a criterion is given for the power spectral density to be bounded on this interval. Second, the use of an alternative power spectral density function that can be deﬁned for the case where a signal consists of a sum of orthogonal or disjoint waveforms is discussed. ...