# Signal processing

Signal transmission using electronic signal processing. Transducers convert signals from other physical waveforms to electric current or voltage waveforms, which then are processed, transmitted as electromagnetic waves, received and converted by another transducer to final form.
File:Cosine Series Plus Noise.png
This signal looks like noise, but the signal processing technique known as the Fourier transform (below), shows that it contains five well defined frequency components.
File:Cosine Series Plus Noise TFM.png
Fourier transform of time domain signal shown above computed with https://sourceforge.net/projects/amoreaccuratefouriertransform/

Signal processing is an enabling technology that encompasses the fundamental theory, applications, algorithms, and implementations of processing or transferring information contained in many different physical, symbolic, or abstract formats broadly designated as signals.[1] It uses mathematical, statistical, computational, heuristic, and linguistic representations, formalisms, and techniques for representation, modelling, analysis, synthesis, discovery, recovery, sensing, acquisition, extraction, learning, security, or forensics.[1]

## History

According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. Oppenheim and Schafer further state that the "digitalization" or digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.[2]

## Application fields of signal processing

In communication systems, signal processing may occur at:

Seismic signal processing

## Categories of signal processing

### Analog signal processing

Analog signal processing is for signals that have not been digitized, as in legacy radio, telephone, radar, and television systems. This involves linear electronic circuits as well as non-linear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators and delay lines. Non-linear circuits include compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.

### Continuous-time signal processing

Continuous-time signal processing is for signals that vary with the change of continuous domain(without considering some individual interrupted points).

The methods of signal processing include: Time domain, Frequency domain, Complex frequency domain. This technology mainly discusses the modeling of linear time-invariant continuous system, integral of system's zero-state response, setting up system function and the continuous time filtering of deterministic signals.

### Discrete-time signal processing

Discrete-time signal processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.

The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.

### Digital signal processing

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 look-up 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 signal processing

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.[5] Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods.

## Notes and references

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2. Oppenheim, Alan V.; Schafer, Ronald W. (1975). Digital Signal Processing. Prentice Hall. p. 5. ISBN 0-13-214635-5.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
3. Boashash, Boualem, ed. (2003). Time frequency signal analysis and processing a comprehensive reference (1 ed.). Amsterdam: Elsevier. ISBN 0-08-044335-4.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
4. P Stoica, R Moses (2005; Chinese Edition, 2007). SPECTRAL ANALYSIS OF SIGNALS (PDF). NJ: Prentice Hall. Check date values in: `|year=` (help)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
5. Billings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley. ISBN 1119943590.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>