Complex Coefficient IIR Digital Filters
Zlatka Nikolova, Georgi K. Stoyanov, Georgi Iliev, Vladimir K. Poulkov · InTech eBooks · 2011
Complex Coefficient IIR Digital Filters -Basic Theory 1.1 IntroductionInterest in complex signal processing goes back quite some time: in 1960 Helstrom (Helstrom, 1960) and Woodward (Woodward, 1960) used the complex envelope presentation to solve problems with signal detection, as did Bello (Bello, 1963), who used it to describe time-invariant linear channels.A number of publications at that time also considered complex signal processing but on a purely theoretical basis.The concept of digital filters with complex coefficients, which will be also referred to as complex filters, was developed by Crystal and Ehrman (Crystal & Ehrman, 1968).This work in fact marks the beginning of interest in complex filters and is one of the most often-cited publications.It demonstrated the increased effectiveness of complex signal processing compared to real signal processing and focused the attention of researchers on that new area of science.This area subsequently progressed well, especially in telecommunications, where the complex representation of signals is very useful as it allows the simple interpretation and realization of quite complicated processing tasks, such as modulation, sampling and quantization.Digital filters with complex coefficients have attracted great interest, owing to their advantages when processing both real and complex signals.As they have both real and imaginary inputs and outputs, the signals they process have to be likewise separated into real and imaginary parts in order to be represented as complex signals.Complex filters have been of theoretical interest for a long time but have only been the subject of intensive experimental investigation over the past two decades, thanks to the rapid development of technology.They have many areas of application, one of the most important being modern telecommunications, which very often uses narrowband signals which are complex in nature (Martin, 2003).Digital complex filters are used to generate SSB (Single Side Band) narrowband signals, typically employed in many wireless telecommunication devices, e.g.SSB transmitters and receivers, complex -modulators, trans-multiplexors, radio-receivers, mobile terminals etc.These devices employ processes such as complex modulation, filtering, mixing, speech analysis and synthesis, and adaptive filtering.Complex filtering is also preferred when DFT (Discrete Fourier Transform) is carried out, as it is a linear combination of complex components.This type of processing is required for high-speed wireless standards.Many of the research problems associated with complex digital filtering have been successfully solved but scientific and technological advances challenge researchers with new problems or require new and better solutions to existing problems.9 www.intechopen.