Signal processing

Signal processing is an area of electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time to perform useful operations on those signals. Depending upon the application, a useful operation could be filtering, spectral analysis, data compression, data transmission, denoising, prediction, smoothing, deblurring, tomographic reconstruction, identification, classification, or a variety of other operations.^[1]

Signals of interest can include sound, images, time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signals are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

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. They 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]

Mathematical topics embraced by signal processing

• Linear signals and systems, and transform theory
• Calculus
• Vector spaces and Linear algebra
• Functional analysis
• Probability and stochastic processes
• Detection theory
• Estimation theory
• Optimization
• Programming
• Numerical methods
• Iterative methods

Categories of signal processing

• Analog signal processing — for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.
• Discrete time signal processing — for sampled signals that are considered as 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 — for signals that have been digitized. 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, Wiener filter and Kalman filter.

Fields of signal processing

• Statistical signal processing — analyzing and extracting information from signals based on their statistical properties
• Audio signal processing — for electrical signals representing sound, such as speech or music
• Speech signal processing — for processing and interpreting spoken words
• Image processing — in digital cameras, computers, and various imaging systems
• Video processing — for interpreting moving pictures
• Array processing — for processing signals from arrays of sensors
• Filtering - used in many fields to process signals
• Seismic signal processing

Typical operations and applications

Processing of signals includes the following operations and algorithms with application examples:

• filtering (for example in tone controls, equalizers and image enhancement software)
• adaptive filtering (for example for echo-cancellation in a conference telephone, or separation of information from noise for aircraft identification by radar)
• spectrum analysis (for example in magnetic resonance imaging and OFDM modulation)
• digitalization, reconstruction and compression (for example, image compression, sound coding)
• storage (in digital delay lines and reverb).
• feature extraction (for example speech-to-text conversion)
• wavetable synthesis (in modems and music synthesizers).

In communication systems, signal processing may occur at OSI layer 1, the Physical Layer (modulation, equalization, multiplexing, radio transmission, etc) in the seven layer OSI model, as well as at OSI layer 6, the Presentation Layer (source coding, including analog-to-digital conversion and data compression).

Notes and references