Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity A digital system uses discrete (discontinuous values usually but not always Symbolized Numerically (hence called "digital" to represent information for DSP and analog signal processing are subfields of signal processing. Analog signal processing is any Signal processing conducted on Analog signals by analog means Signal processing is the analysis interpretation and manipulation of signals Signals of interest include sound, images, biological signals such as DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, biomedical signal processing, seismic data processing, etc. Audio signal processing, sometimes referred to as audio processing, is the processing of a representation of auditory signals, or Sound. Speech signal processing refers to the acquisition manipulation storage transfer and output of human utterances by a computer Digital image processing is the use of computer Algorithms to perform Image processing on Digital images As a subfield of Digital signal processing

Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to Often, the required output signal is another analog output signal, which requires a digital to analog converter. In Electronics, a digital-to-analog converter ( DAC or D-to-A) is a device for converting a digital (usually binary code to an Analog signal

DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), or on purpose-built hardware such as application-specific integrated circuit (ASICs). In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation A digital signal processor ( DSP or DSP micro) is a specialized Microprocessor designed specifically for Digital signal processing, generally Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others. A microprocessor incorporates most or all of the functions of a Central processing unit (CPU on a single Integrated FPGAs should not be confused with the Flip-chip pin grid array, a form of integrated circuit packaging A digital signal controller (DSC can be thought of as a hybrid of Microcontrollers and DSP processors. Stream processing is a Computer programming paradigm related to SIMD, that allows some applications to more easily exploit a limited form of parallel processing ^[1]

DSP domains

In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. Time domain is a term used to describe the analysis of mathematical functions or physical signals with respect to Time. Frequency domain is a term used to describe the analysis of Mathematical functions or signals with respect to frequency Autocorrelation is a mathematical tool for finding repeating patterns such as the presence of a periodic signal which has been buried under noise or identifying the Missing fundamental A wavelet is a mathematical function used to divide a given function or continuous-time signal into different frequency components and study each component with a resolution They choose the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. In Mathematics, the discrete Fourier transform (DFT is one of the specific forms of Fourier analysis. Familiar concepts associated with a Frequency are colors musical notes radio/TV channels and even the regular rotation of the earth Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space. In Signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them

Signal sampling

Main article: Sampling (signal processing)

With the increasing use of computers the usage of and need for digital signal processing has increased. In Signal processing, sampling is the reduction of a Continuous signal to a Discrete signal. A computer is a Machine that manipulates data according to a list of instructions. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to Sampling is usually carried out in two stages, discretization and quantization. In Mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In Mathematics, given a set X and an Equivalence relation ~ on X, the equivalence class of an element a in X In the quantization stage the representative signal values are approximated by values from a finite set.

In order for a sampled analog signal to be exactly reconstructed, the Nyquist-Shannon sampling theorem must be satisfied. The Nyquist–Shannon sampling theorem is a fundamental result in the field of Information theory, in particular Telecommunications and Signal processing This theorem states that the sampling frequency must be greater than twice the bandwidth of the signal. Sampling theorem The Nyquist–Shannon sampling theorem states that perfect reconstruction In practice, the sampling frequency is often significantly more than twice the required bandwidth. The most common bandwidth scenarios are: DC - BW_x (baseband); and F_c +/-BW_x, a frequency band centered on a carrier frequency ("direct demodulation"). In Signal processing, baseband is an adjective that describes signals and systems whose range of Frequencies is measured from zero to a maximum bandwidth

A digital to analog converter (DAC) is used to convert the digital signal back to analog. In Electronics, a digital-to-analog converter ( DAC or D-to-A) is a device for converting a digital (usually binary code to an Analog signal The use of a digital computer is a key ingredient in digital control systems. Digital control is a branch of Control theory that uses Digital Computers to act as a system

Time and space domains

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:

• A "linear" filter is a linear transformation of input samples; other filters are "non-linear. In Mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two Vector spaces that " Linear filters satisfy the superposition condition, i. e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.

• A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.

• A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time. An adaptive filter is a filter that self-adjusts its Transfer function according to an optimizing algorithm

• Some filters are "stable", others are "unstable". A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter produces output which diverges.

• A "finite impulse response" (FIR) filter uses only the input signal, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. A finite impulse response (FIR filter is a type of a Digital filter. IIR redirects here For the conference company IIR see Informa. FIR filters are always stable, while IIR filters may be unstable.

Most filters can be described in Z-domain (a superset of the frequency domain) by their transfer functions. A transfer function is a mathematical representation in terms of spatial or temporal frequency of the relation between the input and output of a ( linear time-invariant) A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response. "Difference equation" redirects here It should not be confused with a Differential equation. In Complex analysis, a zero of a Holomorphic function f is a Complex number a such that f ( a) = 0 In Complex analysis, a pole of a Meromorphic function is a certain type of singularity that behaves like the singularity at z = 0 The impulse response of a system is its output when presented with a very brief input signal an impulse The step response of a system in a given initial state consists of the time evolution of its Outputs when its control inputs are Heaviside step functions The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. In Mathematics and in particular Functional analysis, convolution is a mathematical operation on two functions f and The impulse response of a system is its output when presented with a very brief input signal an impulse Filters can also be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation

Frequency domain

Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.

The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing.

Filtering, particularly in non realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filters. In Signal processing, a sinc filter is an idealized filter that removes all frequency components above a given bandwidth leaves the low frequencies alone and has

There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. A cepstrum (ˈkɛpstrəm is the result of taking the Fourier transform (FT of the decibel spectrum as if it were a signal This emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components.

Frequency domain analysis is also called spectrum- or spectral analysis.

Applications

The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology, and biomedicine. Audio signal processing, sometimes referred to as audio processing, is the processing of a representation of auditory signals, or Sound. Digital image processing is the use of computer Algorithms to perform Image processing on Digital images As a subfield of Digital signal processing Video compression refers to reducing the quantity of Data used to represent video images and is a straightforward combination of Image compression and Motion Speech processing is the study of speech signals and the processing methods of these signals Speech recognition (also known as automatic speech recognition or computer speech recognition) converts spoken words to machine-readable input (for example to keypresses Digital communications refers to the transmission of a sequence of Digital messages (a Bit stream) or a digitized analog signal Radar is a system that uses electromagnetic waves to identify the range altitude direction or speed of both moving and fixed objects such as Aircraft, ships Sonar (which started as an Acronym for sound navigation and ranging) is a technique that uses Sound propagation (usually underwater to navigate Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in Hifi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers. High fidelity or hi-fi reproduction is a term used by home stereo listeners and home audio enthusiasts ( Audiophiles to refer to high-quality reproduction A sound reinforcement system is an arrangement of Microphones electronic Signal processors Amplifiers and Loudspeakers that makes live or pre-recorded Weather forecasting is the application of science and technology to predict the state of the atmosphere for a future time and a given location Economic forecasting is the process of making predictions about the economy as a whole or in part Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes Industrial processes are procedures involving chemical or mechanical steps to aid in the Manufacture of an item or items usually carried out on a very The bouncing ball animation (below consists of these 6 frames Medical imaging refers to the techniques and processes used to create Images of the human body (or parts thereof for clinical purposes ( Medical procedures seeking to Computer graphics are Graphics created by Computers and more generally the Representation and Manipulation of Pictorial Data For the album by The Jam see Sound Affects. Sound effects or audio effects are artificially created or enhanced Sounds An electric guitar is a type of Guitar that uses pickups to convert the vibration of its steel-cored strings into an electrical current which is made louder Generally an amplifier or simply amp, is any device that changes usually increases the amplitude of a signal.

Implementation

Digital signal processing is often implemented using specialised microprocessors such as the DSP56000 and the TMS320. A digital signal processor ( DSP or DSP micro) is a specialized Microprocessor designed specifically for Digital signal processing, generally The Motorola DSP56000 (aka 56K) is a family of DSP chips produced by Motorola Semiconductor (now known as Freescale Semiconductor) starting in Texas Instruments TMS320 is a blanket name for a series of Digital signal processors (DSPs from Texas Instruments. These often process data using fixed-point arithmetic, although some versions are available which use floating point arithmetic and are more powerful. In Computing, a fixed-point number representation is a Real data type for a number that has a fixed number of digits after (and sometimes also before the In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number. For faster applications FPGAs^[2] might be used. FPGAs should not be confused with the Flip-chip pin grid array, a form of integrated circuit packaging Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and startup Stream Processors, Inc. Freescale Semiconductor Inc is an American Semiconductor manufacturer Stream Processors Inc is a Silicon Valley -based Fabless semiconductor company specializing in the design and manufacture of high-performance Digital signal For faster applications with vast usage, ASICs might be designed specifically. For slow applications such as flame scanning, a traditional slower processor such as a microcontroller can cope.

Techniques

Related fields

• Automatic control
• Computer Science
• Data compression
• Electrical engineering
• Information theory
• Telecommunication
• Analog signal processing

References

Further reading

External links

• The Scientist and Engineer's Guide to Digital Signal Processing, a book on DSP with all content available online, by Steven W. Smith, Ph. D.
• Digital Signal Processing Wikibook