# Digital signal processing

**DSPsignal processingdigital signal processing (DSP)digitalDigital Signal Processorsdigital transformDSP (Digital Signal Processing)processingsignalspatial domain**

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.wikipedia

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### Digital signal processor

**DSPDSPsdigital signal processors**

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.

A digital signal processor (DSP) is a specialized microprocessor (or a SIP block), with its architecture optimized for the operational needs of digital signal processing.

### Analog signal processing

**analoganalog-control voltages**

Digital signal processing and analog signal processing are subfields of signal processing.

Analog signal processing is a type of signal processing conducted on continuous analog signals by some analog means (as opposed to the discrete Digital Signal Processing where the signal processing is carried out by a digital process).

### Speech processing

**Speechspeech signal processingmachine processing of speech**

DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, seismology, among others. Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine.

The signals are usually processed in a digital representation, so speech processing can be regarded as a special case of digital signal processing, applied to speech signals.

### Radar

**radar stationradarsradar system**

DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, seismology, among others. Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine.

High tech radar systems are associated with digital signal processing, machine learning and are capable of extracting useful information from very high noise levels.

### Digital image processing

**image processingimageprocessing**

DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, seismology, among others. Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine.

As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.

### Nyquist–Shannon sampling theorem

**sampling theoremsampling theoryNyquist**

The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal.

In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals").

### Quantization (signal processing)

**quantizationquantization errorquantized**

Sampling is usually carried out in two stages, discretization and quantization. Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling.

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements.

### Discrete Fourier transform

**DFTcircular convolution theoremFourier transform**

They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain representation.

In digital signal processing, the function is any quantity or signal that varies over time, such as the pressure of a sound wave, a radio signal, or daily temperature readings, sampled over a finite time interval (often defined by a window function ).

### Audio signal processing

**audio processingaudio processorsound processing**

flanger - to create an unusual sound, a delayed signal is added to the original signal with a continuously variable delay (usually smaller than 10 ms). This effect is now done electronically using DSP, but originally the effect was created by playing the same recording on two synchronized tape players, and then mixing the signals together. As long as the machines were synchronized, the mix would sound more-or-less normal, but if the operator placed his finger on the flange of one of the players (hence "flanger"), that machine would slow down and its signal would fall out-of-phase with its partner, producing a phasing effect. Once the operator took his finger off, the player would speed up until its tachometer was back in phase with the master, and as this happened, the phasing effect would appear to slide up the frequency spectrum. This phasing up-and-down the register can be performed rhythmically.

### Sampling (signal processing)

**sampling ratesamplingsample rate**

The signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling.

However, digital signal processing operations can have very high dynamic range, consequently it is common to perform mixing and mastering operations at 32-bit precision and then convert to 16- or 24-bit for distribution.

### Discrete time and continuous time

**discrete-timediscrete timecontinuous-time**

Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling.

Discrete-time signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.

### Spectral density estimation

**spectral estimationfrequency estimationspectral analysis**

DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, seismology, among others.

Frequency estimation is the process of estimating the complex frequency components of a signal in the presence of noise given assumptions about the number of the components.

### Convolution

**convolvedconvolvingkernel**

The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response.

Digital signal processing and other applications typically use fast convolution algorithms to reduce the cost of the convolution to O( log ) complexity.

### Digital synthesizer

**Digitaldigital synthesizersdigital synthesis**

Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine.

A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds.

### Impulse response

**impulseImpulse Response Functionsimpulse-response function.**

The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response. A filter may also be described as a difference equation, a collection of zeros and poles or an impulse response or step response.

Impulse response analysis is a major facet of radar, ultrasound imaging, and many areas of digital signal processing.

### Frequency domain

**frequency-domainfrequencyspectral analysis**

Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, and spatio-temporal domains.

Z transform – discrete-time signals, digital signal processing

### Stream processing

**stream processorsstream processorstream programming**

Additional technologies for digital signal processing include more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors.

Stream processing is essentially a compromise, driven by a data-centric model that works very well for traditional DSP or GPU-type applications (such as image, video and digital signal processing) but less so for general purpose processing with more randomized data access (such as databases).

### Bilinear transform

**bilinearitytransform**

Bilinear transform

The bilinear transform (also known as Tustin's method) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

### Recurrence relation

**difference equationdifference equationsrecurrence**

A filter may also be described as a difference equation, a collection of zeros and poles or an impulse response or step response.

In digital signal processing, recurrence relations can model feedback in a system, where outputs at one time become inputs for future time.

### Analog-to-digital converter

**ADCanalog to digital converteranalog-to-digital conversion**

To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter (ADC).

Digital signal processing

### Fast Fourier transform

**FFTFast Fourier Transform (FFT)Fourier**

This is essentially no different from any other data processing, except DSP mathematical techniques (such as the FFT) are used, and the sampled data is usually assumed to be uniformly sampled in time or space.

This huge improvement made the calculation of the DFT practical; FFTs are of great importance to a wide variety of applications, from digital signal processing and solving partial differential equations to algorithms for quick multiplication of large integers.

### Goertzel algorithm

Goertzel algorithm

The Goertzel algorithm is a technique in digital signal processing (DSP) that provides a means for efficient evaluation of individual terms of the discrete Fourier transform (DFT), thus making it useful in certain practical applications, such as recognition of DTMF tones produced by the buttons pushed on a telephone keypad.

### Equalization (audio)

**equalizationequalizerEQ**

Specific examples include speech coding and transmission in digital mobile phones, room correction of sound in hi-fi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, medical imaging such as CAT scans and MRI, MP3 compression, computer graphics, image manipulation, audio crossovers and equalization, and audio effects units.

In the late 1990s and in the 2000s, parametric equalizers became increasingly available as Digital Signal Processing (DSP) equipment, usually in the form of plug-ins for various digital audio workstations.

### Data transmission

**digital communicationsdata transferdata communication**

Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine.

Transmitting analog signals digitally allows for greater signal processing capability.

### Ronald W. Schafer

**R.W. Schafer**

James H. McClellan, Ronald W. Schafer, Mark A. Yoder: Signal Processing First, Prentice Hall, ISBN: 0-13-090999-8

Ronald W. Schafer (born February 17, 1938) is an electrical engineer notable for his contributions to digital signal processing.