By Boaz Porat

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A accomplished, functional and up to date exposition on electronic sign processing. either mathematical and precious, this e-book makes use of a rigorous method of support readers research the speculation and perform of DSP. It discusses useful spectral research, together with using home windows for spectral research, sinusoidal sign research, and the impression of noise. It additionally covers FIR and IIR filters, together with particular layout approaches and MATLAB instruments.

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Signals (a) We denote the real line by ~, the complex plane by (, and the set of integers byiL (b) In general, we denote temporal signals by lowercase letters. , functions on the real line) are denoted with their arguments in round parentheses; for example: x(t), y(t), and so on. , sequences, or functions on the integers) are denoted with their arguments in square brackets; for example: x [n], y [n], and so on. (e) Let the continuous-time signal xU) be defined on the interval [0, T]. periodic extension on the real line is denoted as Its x(t) = x(t mod T).

Discrete-time periodic signals and discrete-time random signals are defined in a manner similar to the corresponding continuous-time signals and share similar properties. The material in this chapter is covered in many books. For general signals and system theory, see Oppenheim and Willsky [1983], Gabel and Roberts [1987], Kwakernaak and Sivan [1991], or Haykin and Van Veen [1997]. For random signals and their relation to linear systems, see Papoulis [1991] or Gardner [1986]. (d) Various combinations of the above.

Random signals appear often in real life. Examples include: 1. The noise heard from a radio receiver that is not tuned to an operating channel. 2. The noise heard from a helicopter rotor. 3. Electrical signals recorded from a human brain through electrodes put in contact with the skull (these are called electroencephalograms, or EEGs). 4. Mechanical vibrations sensed in a vehicle moving on a rough terrain. 5. Angular motion of a boat in the sea caused by waves and wind. 5. 5 A continuous-time random signal.

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