Digital signal processing

Source: Wikipedia, the free encyclopedia.
"Digital transform" redirects here. For the impact of digital technology on society, see Digital transformation.

Digital signal processing (DSP) is the use of

pulse train,[1][2] which is typically generated by the switching of a transistor.[3]

Digital signal processing and

telecommunications, control systems, biomedical engineering, and seismology
, among others.

DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification[4] and can be implemented in the time, frequency, and spatio-temporal domains.

The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as

wireless communications.[6] DSP is applicable to both streaming data
and static (stored) data.

Signal sampling

Main article: Sampling (signal processing)

To digitally analyze and manipulate an analog signal, it must be digitized with an

real numbers
to integers is an example.

The

stop band
rejection instead of the original (unfiltered) signal.

Theoretical DSP analyses and derivations are typically performed on

quantization error), created by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an ADC. The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a digital-to-analog converter
(DAC).

Domains

DSP engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains. 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.

Time and space domains

Time domain refers to the analysis of signals with respect to time. Similarly, space domain refers to the analysis of signals with respect to position, e.g., pixel location for the case of image processing.

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. The surrounding samples may be identified with respect to time or space. The output of a linear digital filter to any given input may be calculated by convolving the input signal with an impulse response.

Frequency domain

Main article: Frequency domain

Signals are converted from time or space domain to the frequency domain usually through use of the Fourier transform. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant, 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. Frequency domain analysis is also called spectrum- or spectral analysis.

Filtering, particularly in non-realtime work can also be achieved in the frequency domain, applying the filter and then converting back to the time domain. This can be an efficient implementation and can give essentially any filter response 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 harmonic structure of the original spectrum.

Z-plane analysis

Digital filters come in both infinite impulse response (IIR) and finite impulse response (FIR) types. Whereas FIR filters are always stable, IIR filters have feedback loops that may become unstable and oscillate. The Z-transform provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the Laplace transform, which is used to design and analyze analog IIR filters.

Autoregression analysis

A signal is represented as linear combination of its previous samples. Coefficients of the combination are called autoregression coefficients. This method has higher frequency resolution and can process shorter signals compared to the Fourier transform.[9] Prony's method can be used to estimate phases, amplitudes, initial phases and decays of the components of signal.[10][9] Components are assumed to be complex decaying exponents.[10][9]

Time-frequency analysis

A time-frequency representation of signal can capture both temporal evolution and frequency structure of analyzed signal. Temporal and frequency resolution are limited by the principle of uncertainty and the tradeoff is adjusted by the width of analysis window. Linear techniques such as

autoregressive methods (e.g. segmented Prony method)[10][12][13] are used for representation of signal on the time-frequency plane. Non-linear and segmented Prony methods can provide higher resolution, but may produce undesirable artifacts. Time-frequency analysis is usually used for analysis of non-stationary signals. For example, methods of fundamental frequency estimation, such as RAPT and PEFAC[14]
are based on windowed spectral analysis.

Wavelet

JPEG2000
. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left.

In numerical analysis and functional analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information. The accuracy of the joint time-frequency resolution is limited by the uncertainty principle of time-frequency.

Empirical mode decomposition

Empirical mode decomposition is based on decomposition signal into

intrinsic mode functions (IMFs). IMFs are quasiharmonical oscillations that are extracted from the signal.[15]

Implementation

DSP algorithms may be run on general-purpose computers[16] and digital signal processors.[17] DSP algorithms are also implemented on purpose-built hardware such as application-specific integrated circuit (ASICs).[18] Additional technologies for digital signal processing include more powerful general purpose microprocessors, graphics processing units, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors.[19]

For systems that do not have a

Photoshop
.

When the application requirement is real-time, DSP is often implemented using specialized or dedicated processors or microprocessors, sometimes using multiple processors or multiple processing cores. These may process data using fixed-point arithmetic or floating point. For more demanding applications

FPGAs may be used.[20] For the most demanding applications or high-volume products, ASICs
might be designed specifically for the application.

Parallel implementations of DSP algorithms, utilising multi-core CPU and many-core GPU architectures, are developed to improve the performances in terms of latency of these algorithms.[21]

Native processing is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional third-party DSP chips located on extension cards or external hardware boxes or racks. Many

Cubase, Digital Performer and Pro Tools LE use native processing. Others, such as Pro Tools HD, Universal Audio's UAD-1 and TC Electronic
's Powercore use DSP processing.

Applications

General application areas for DSP include

Specific examples include

MRI, audio crossovers and equalization, digital synthesizers, and audio effects units.[22]

Techniques

Related fields

Further reading

Wikibooks has a book on the topic of: Digital Signal Processing

References

  1. ISBN 9788120319561
    . Digital signals are fixed-width pulses, which occupy only one of two levels of amplitude.
  2. ISBN 9780387204734
    .
  3. ISBN 978-0-07-058831-8
    .
  4. ISBN 978-1-119-94359-4
    .
  5. ISBN 9780750689762
    .
  6. ISBN 9783319011653
    .
  7. doi:10.1109/49.761034
    .
  8. S2CID 1704522
    .
  9. ^
    ISBN 978-0-13-214149-9
    .
  10. ^
    ISSN 0888-3270
    . Retrieved 2019-02-17.
  11. ^ So, Stephen; Paliwal, Kuldip K. (2005). "Improved noise-robustness in distributed speech recognition via perceptually-weighted vector quantisation of filterbank energies". Ninth European Conference on Speech Communication and Technology.
  12. S2CID 130300729
    .
  13. S2CID 226638723
    . Retrieved 2020-09-08.
  14. S2CID 13161793
    . Retrieved 2017-12-03.
  15. S2CID 1262186
    . Retrieved 2018-06-05.
  16. S2CID 17594911
    .
  17. S2CID 236187914
    .
  18. doi:10.1016/j.jksuci.2023.101574
    .
  19. ISBN 0-7506-6344-8
    .
  20. ^ JPFix (2006). "FPGA-Based Image Processing Accelerator". Retrieved 2008-05-10.
  21. S2CID 211686462
    .
  22. ISBN 978-0139141010
    .
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