Present-day communications systems are quite complex. In the early days of communication, one just needed a modulator for signal to be transmitted, a radio-frequency (r.f.) amplifier, and the antenna. On the receiving side, one needed a receiving antenna, a preamplifier, and a demodulator. Because of the wireless communication which involves networking, the complexity is steadily growing and it will continue to do so to accommodate wireless access to the Internet and multimedia. Figure 8.1.1 shows the block diagram of a digital communication system. Source encoding, also called data compression, removes the redundancy of the source by representing of the data using the smallest number of binary digits [Pro95]. In many cases, specially for secure Internet traffic, for an example, one uses encryption so that unauthorized detection of signal can be minimized or avoided. In contrast to the source coding which removes redundancy, channel coding introduces some redundancy in a predetermined fashion to improve the fidelity of the signal output. The channel has noise and interference, which causes error in the output. By introducing an n-bit codeword for a k-bit of information when n>k, the bit error rate (BER) can be drastically reduced. The digital modulator maps the binary output of the channel encoder to electrical signal waveforms. The modulator could be binary or M-ary, as also amplitude, phase, or frequency modulated or a combination of them.

Applications of Subband and Wavelet Transform in Digital Communications

In this chapter, we will discuss various methods which can be used to realize wavelet and subband transforms for practical applications. It is impossible to give an all-inclusive description of every possible architecture for implementation of wavelet transforms; we will, instead, mention some significant results in digital electronic chip design, optical systems, and hybrid optical-electronic systems.

Real-Time Implementations of the Wavelet Transform

This paper discusses a new method for performing wavelet-based pattern recognition and feature extraction. Known as 'progressive pattern recognition,' this approach is based on performing a subband transform of a target image and then performing partial correlations with different subband resolutions; it is possible to recognize the image without correlating against the complete wavelet transform, thereby realizing considerable savings in computational time. Computer simulations of palm print recognition are presented, and extensions to both scale and rotation invariant systems and optical implementations are discussed.

A. Abbatte

Papers

Wavelet image processing for optical pattern recognition and feature extraction