Digital signal processing (DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. 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.
Since the goal of DSP is usually to measure or filter continuous realworld analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analogtodigital converter (ADC). Often, the required output signal is another analog output signal, which requires a digitaltoanalog converter (DAC). Even if this process is more complex than analog processing and has a discrete value range, the stability of digital signal processing thanks to error detection and correction and being less vulnerable to noise makes it advantageous over analog signal processing for many, though not all, applications.^{[1]}
DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), or on purposebuilt hardware such as applicationspecific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, fieldprogrammable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.^{[2]}
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In DSP, engineers usually study digital signals in one of the following domains: time domain (onedimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. 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. Autocorrelation is defined as the crosscorrelation of the signal with itself over varying intervals of time or space.
With the increasing use of computers the usage of and need for digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analogtodigital converter. Sampling is usually carried out in two stages, discretization and quantization. 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 the quantization stage the representative signal values are approximated by values from a finite set.
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 of the signal. In practice, the sampling frequency is often significantly more than twice the required bandwidth.
A digitaltoanalog converter is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient in digital control systems.
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:
Most filters can be described in Zdomain (a superset of the frequency domain) by their transfer functions. 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. The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. 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.
Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. 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 nonrealtime 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.
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. 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.
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. 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, computergenerated animations in movies, medical imaging such as CAT scans and MRI, MP3 compression, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers.
Digital signal processing is often implemented using specialised microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixedpoint arithmetic, although some versions are available which use floating point arithmetic and are more powerful. For faster applications FPGAs^{[3]} might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate.


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converts analog signal to digital, then DAC returns it back to analog format after processing]]
Digital signal processing (DSP) is concerned with the processing of digital signals or analog signals after converting from analog to digital format. DSP includes subfields like: communication signals processing, radar signal processing, sensor array processing, digital image processing, etc.
DSP is usually used with realworld analog signals found in our lives, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another realworld analog signal, which requires a digital to analog converter.
Digital signal processing algorithms can run on:^{[1]}
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