Abstract
Transform-domain processing of signals has been successfully used for several decades in many engineering fields spanning the application areas from communications to oil exploration. The most popular block transform has been the discrete Fourier transform (DFT), which found a variety of applications because of its performance and low cost of implementation, i.e., fast Fourier transform (FFT). More recently, the discrete cosine transform (DCT) has become the industry standard for still frame image and video compression applications, e.g., JPEG, H.261, H.263, and MPEG compression algorithms. The subband transform with its multiresolution feature has also been forwarded as an alternative to the DCT for low bit rate image and video coding. In addition to these conventional applications of transform-domain signal processing, there has been a rapidly growing activity in new application areas—namely, spread spectrum communication, discrete multitone (DMT) modulation, low probability of intercept (LPI) communication, radar signal processing, biomedical signal processing, and many others. The chapter demonstrates the way the fundamental concepts of linear transforms can lead to meaningful applications in representable areas, including subband coding, interference excision in spread spectrum communications, discrete multitone modulation, and orthogonal code division multiple access (CDMA) user codes.
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