mathematical basis for digital signal processing, without taking quantization error into consideration. Digital Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and lookup tables. Examples of algorithms are the fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters. Nonlinear Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains. Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods. Polynomial signal processing is a type of non-linear signal processing, where polynomial systems may be interpreted as conceptually straight forward extensions of linear systems to the non-linear case. Statistical Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. Statistical techniques are widely used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, and construct techniques based on this model to reduce the noise in the resulting image. Application fields Audio signal processing for electrical signals representing sound, such as speech or music Image processing in digital cameras, computers and various imaging systems Video processing for interpreting moving pictures Wireless communication waveform generations, demodulation, filtering, equalization Control systems Array processing for processing signals from arrays of sensors Process control a variety of signals are used, including the industry standard 4-20 mA current loop Seismology Financial signal processing analyzing financial data using signal processing techniques, especially for prediction purposes. Feature extraction, such as image understanding and speech recognition. Quality improvement, such as noise reduction, image enhancement, and echo cancellation. Source coding including audio compression, image compression, and video compression. Genomic signal processing In geophysics, signal processing is used to amplify the signal vs the noise within time-series measurements of geophysical data. Processing is conducted within either the time domain or frequency domain, or both. In communication systems, signal processing may occur at: OSI layer 1 in the seven-layer OSI model, the