-DIGITAL SIGNAL PROCESSING- - -KINGDOM OF JOGA-

-as of [28 DECEMBER 2023]–

*aka [DSP]*

-‘digital signal processing’ 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’-

The digital 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.

In digital electronics, a digital signal is represented as a pulse train,[1][2] which is typically generated by the switching of a transistor

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include

audio and speech processing,

sonar,

radar and other sensor array processing,

spectral density estimation,

statistical signal processing,

digital image processing,

data compression,

video coding,

audio coding,

image compression,

signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others

DSP can involve linear or nonlinear operations.

Nonlinear signal processing is closely related to ‘non-linear system identification’ 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 error detection and correction in transmission as well as data compression

Digital signal processing is also fundamental to digital technology, such as digital telecommunication and wireless communications.[6]

DSP is applicable to both streaming data and static (stored) data

Signal sampling

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

Sampling is usually carried out in two stages, discretization and quantization.

Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude

Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding real numbers to integers is an example.

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 practice, the sampling frequency is often significantly higher than this.[8]

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. 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[edit]
In 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[edit]
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[edit]
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[edit]
Digital filters come in both IIR and 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[edit]
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[edit]
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 Short-time Fourier transform, wavelet transform, filter bank,[11] non-linear (e.g., Wigner — Ville transform[10]) and 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 undesireable artefacts. 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[edit]

An example of the 2D discrete wavelet transform that is used in 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[edit]
Empirical mode decomposition is based on decomposition signal into intrinsic mode functions (IMF). IMFs are quasiharmonical oscillations that are extracted from the signal.[15]

Implementation[edit]
DSP algorithms may be run on general-purpose computers and digital signal processors. DSP algorithms are also implemented on purpose-built hardware such as application-specific integrated circuit (ASICs). 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.[16]

For systems that do not have a real-time computing requirement and the signal data (either input or output) exists in data files, processing may be done economically with a general-purpose computer. This is essentially no different from any other data processing, except DSP mathematical techniques (such as the DCT and FFT) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. An example of such an application is processing digital photographs with software such as 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.[17] For the most demanding applications or high-volume products, ASICs might be designed specifically for the application.

Applications[edit]
General application areas for DSP include

Audio signal processing
Audio data compression e.g. MP3
Video data compression
Computer graphics
Digital image processing
Photo manipulation
Speech processing
Speech recognition
Data transmission
Radar
Sonar
Financial signal processing
Economic forecasting
Seismology
Biomedicine
Weather forecasting
Specific examples include speech coding and transmission in digital mobile phones, room correction of sound in hi-fi and sound reinforcement applications, analysis and control of industrial processes, medical imaging such as CAT scans and MRI, audio crossovers and equalization, digital synthesizers, and audio effects units.[18]

Techniques[edit]

Bilinear transform

Discrete Fourier transform

Discrete-time Fourier transform

Filter design

Goertzel algorithm

LTI system theory

Minimum phase

s-plane

Transfer function

Z-transform

[edit]

Analog signal processing

Automatic control

Computer engineering

Computer science

Data compression

Dataflow programming

Discrete cosine transform

Electrical engineering

Fourier analysis

Information theory

Machine learning

Real-time computing

Stream processing

Telecommunication

Time series

Wavelet

References[edit]

^ B. SOMANATHAN NAIR (2002). Digital electronics and logic design. PHI Learning Pvt. Ltd. p. 289. ISBN 9788120319561. Digital signals are fixed-width pulses, which occupy only one of two levels of amplitude.

^ Joseph Migga Kizza (2005). Computer Network Security. Springer Science & Business Media. ISBN 9780387204734.

^ 2000 Solved Problems in Digital Electronics. Tata McGraw-Hill Education. 2005. p. 151. ISBN 978-0-07-058831-8.

^ Billings, Stephen A. (Sep 2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. UK: Wiley. ISBN 978-1-119-94359-4.

^ Broesch, James D.; Stranneby, Dag; Walker, William (2008-10-20). Digital Signal Processing: Instant access (1 ed.). Butterworth-Heinemann-Newnes. p. 3. ISBN 9780750689762.

^ Srivastava, Viranjay M.; Singh, Ghanshyam (2013). MOSFET Technologies for Double-Pole Four-Throw Radio-Frequency Switch. Springer Science & Business Media. p. 1. ISBN 9783319011653.

^ Walden, R. H. (1999). “Analog-to-digital converter survey and analysis”. IEEE Journal on Selected Areas in Communications. 17 (4): 539–550. doi:10.1109/49.761034.

^ Candes, E. J.; Wakin, M. B. (2008). “An Introduction To Compressive Sampling”. IEEE Signal Processing Magazine. 25 (2): 21–30. Bibcode:2008ISPM…25…21C. doi:10.1109/MSP.2007.914731. S2CID 1704522.

^ Jump up to: a b c Marple, S. Lawrence (1987-01-01). Digital Spectral Analysis: With Applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 978-0-13-214149-9.

^ Jump up to: a b c d Ribeiro, M.P.; Ewins, D.J.; Robb, D.A. (2003-05-01). “Non-stationary analysis and noise filtering using a technique extended from the original Prony method”. Mechanical Systems and Signal Processing. 17 (3): 533–549. Bibcode:2003MSSP…17..533R. doi:10.1006/mssp.2001.1399. ISSN 0888-3270. Retrieved 2019-02-17.

^ 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.

^ Mitrofanov, Georgy; Priimenko, Viatcheslav (2015-06-01). “Prony Filtering of Seismic Data”. Acta Geophysica. 63 (3): 652–678. Bibcode:2015AcGeo..63..652M. doi:10.1515/acgeo-2015-0012. ISSN 1895-6572. S2CID 130300729.

^ Mitrofanov, Georgy; Smolin, S. N.; Orlov, Yu. A.; Bespechnyy, V. N. (2020). “Prony decomposition and filtering”. Geology and Mineral Resources of Siberia (2): 55–67. doi:10.20403/2078-0575-2020-2-55-67. ISSN 2078-0575. S2CID 226638723. Retrieved 2020-09-08.

^ Gonzalez, Sira; Brookes, Mike (February 2014). “PEFAC – A Pitch Estimation Algorithm Robust to High Levels of Noise”. IEEE/ACM Transactions on Audio, Speech, and Language Processing. 22 (2): 518–530. doi:10.1109/TASLP.2013.2295918. ISSN 2329-9290. S2CID 13161793. Retrieved 2017-12-03.

^ Huang, N. E.; Shen, Z.; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q.; Yen, N.-C.; Tung, C. C.; Liu, H. H. (1998-03-08). “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 454 (1971): 903–995. Bibcode:1998RSPSA.454..903H. doi:10.1098/rspa.1998.0193. ISSN 1364-5021. S2CID 1262186. Retrieved 2018-06-05.

^ Stranneby, Dag; Walker, William (2004). Digital Signal Processing and Applications (2nd ed.). Elsevier. ISBN 0-7506-6344-8.

^ JPFix (2006). “FPGA-Based Image Processing Accelerator”. Retrieved 2008-05-10.

^ Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, NJ: Prentice-Hall, Inc. ISBN 978-0139141010.