SherbyNet - /page/wikibook/entry.mu

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`!Signal processing`! is an `F33f`_`[electrical engineering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electrical_engineering]`_`f subfield that focuses on analyzing, modifying and synthesizing `*`F33f`_`[signals`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Signal]`_`f`*, such as `F33f`_`[sound`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Audio_signal_processing]`_`f, `F33f`_`[images`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Image_processing]`_`f, `F33f`_`[potential fields`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Scalar_potential]`_`f, `F33f`_`[seismic signals`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Seismic_tomography]`_`f, `F33f`_`[altimetry processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Altimeter]`_`f, and `F33f`_`[scientific measurements`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Scientific_measurements]`_`f.`:cite-ref-1[`F5bf`_`[1`#cite-note-1]`_`f] Signal processing techniques are used to optimize transmissions, `F33f`_`[digital storage`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Data_storage]`_`f efficiency, correcting distorted signals, improve `F33f`_`[subjective video quality`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Subjective_video_quality]`_`f, and to detect or pinpoint components of interest in a measured signal.`:cite-ref-2[`F5bf`_`[2`#cite-note-2]`_`f]

>>Contents

• `F0af`_`[History`#history]`_`f

• `F0af`_`[Definition of a signal`#definition-of-a-signal]`_`f

• `F0af`_`[Categories`#categories]`_`f

• `F0af`_`[Analog`#analog]`_`f

• `F0af`_`[Continuous time`#continuous-time]`_`f

• `F0af`_`[Discrete time`#discrete-time]`_`f

• `F0af`_`[Digital`#digital]`_`f

• `F0af`_`[Nonlinear`#nonlinear]`_`f

• `F0af`_`[Statistical`#statistical]`_`f

• `F0af`_`[Graph`#graph]`_`f

• `F0af`_`[Application fields`#application-fields]`_`f

• `F0af`_`[Typical devices`#typical-devices]`_`f

• `F0af`_`[Mathematical methods applied`#mathematical-methods-applied]`_`f

• `F0af`_`[See also`#see-also]`_`f

• `F0af`_`[References`#references]`_`f

• `F0af`_`[Further reading`#further-reading]`_`f

• `F0af`_`[External links`#external-links]`_`f

-─

>>History

According to `F33f`_`[Alan V. Oppenheim`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Alan_V._Oppenheim]`_`f and `F33f`_`[Ronald W. Schafer`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Ronald_W._Schafer]`_`f, the principles of signal processing can be found in the classical `F33f`_`[numerical analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Numerical_analysis]`_`f techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital `F33f`_`[control systems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Control_system]`_`f of the 1940s and 1950s.`:cite-ref-3[`F5bf`_`[3`#cite-note-3]`_`f]

In 1948, `F33f`_`[Claude Shannon`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Claude_Shannon]`_`f wrote the influential paper "`F33f`_`[A Mathematical Theory of Communication`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=A_Mathematical_Theory_of_Communication]`_`f" which was published in the `*`F33f`_`[Bell System Technical Journal`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bell_System_Technical_Journal]`_`f`*.`:cite-ref-4[`F5bf`_`[4`#cite-note-4]`_`f] The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.`:cite-ref-fifty-5-0[`F5bf`_`[5`#cite-note-fifty-5]`_`f]

Signal processing matured and flourished in the 1960s and 1970s, and `F33f`_`[digital signal processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Digital_signal_processing]`_`f became widely used with specialized `F33f`_`[digital signal processor`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Digital_signal_processor]`_`f chips in the 1980s.`:cite-ref-fifty-5-1[`F5bf`_`[5`#cite-note-fifty-5]`_`f]

>>Definition of a signal

A signal is a `F33f`_`[function`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Function_(mathematics)]`_`f x ( t ) {\\displaystyle x(t)} , where this function is either`:cite-ref-6[`F5bf`_`[6`#cite-note-6]`_`f]

• deterministic (then one speaks of a deterministic signal) or

• a path ( x t ) t ∈ ∈ T {\\displaystyle (x_{t})_{t\\in T}} , a realization of a `F33f`_`[stochastic process`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stochastic_process]`_`f ( X t ) t ∈ ∈ T {\\displaystyle (X_{t})_{t\\in T}}

>>Categories

>>>Analog

Analog signal processing is for signals that have not been digitized, as in most 20th-century `F33f`_`[radio`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Radio]`_`f, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, `F33f`_`[passive filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Passive_filter]`_`f, `F33f`_`[active filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Active_filter]`_`f, `F33f`_`[additive mixers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electronic_mixer]`_`f, `F33f`_`[integrators`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Integrator]`_`f, and `F33f`_`[delay lines`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Analog_delay_line]`_`f. Nonlinear circuits include `F33f`_`[compandors`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Compandor]`_`f, multipliers (`F33f`_`[frequency mixers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Frequency_mixer]`_`f, `F33f`_`[voltage-controlled amplifiers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Voltage-controlled_amplifier]`_`f), `F33f`_`[voltage-controlled filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Voltage-controlled_filter]`_`f, `F33f`_`[voltage-controlled oscillators`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Voltage-controlled_oscillator]`_`f, and `F33f`_`[phase-locked loops`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Phase-locked_loop]`_`f.

>>>Continuous time

`F33f`_`[Continuous-time signal`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Continuous_signal]`_`f processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points).

The methods of signal processing include `F33f`_`[time domain`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Time_domain]`_`f, `F33f`_`[frequency domain`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Frequency_domain]`_`f, and `F33f`_`[complex frequency domain`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Complex_frequency]`_`f. This technology mainly discusses the modeling of a `F33f`_`[linear time-invariant`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_time-invariant]`_`f continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals. For example, in time domain, a continuous-time signal x ( t ) {\\displaystyle x(t)} passing through a `F33f`_`[linear time-invariant`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_time-invariant]`_`f filter/system denoted as h ( t ) {\\displaystyle h(t)} , can be expressed at the output as

y ( t ) = ∫ ∫ − − ∞ ∞ ∞ ∞ h ( τ τ ) x ( t − − τ τ ) d τ τ {\\displaystyle y(t)=\\int _{-\\infty }^{\\infty }h(\\tau )x(t-\\tau )\\,d\\tau }

In some contexts, h ( t ) {\\displaystyle h(t)} is referred to as the impulse response of the system. The above `F33f`_`[convolution`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Convolution]`_`f operation is conducted between the input and the system.

>>>Discrete time

`F33f`_`[Discrete-time signal`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Discrete-time_signal]`_`f processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

`*Analog discrete-time signal processing`* is a technology based on electronic devices such as `F33f`_`[sample and hold`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sample_and_hold]`_`f circuits, analog time-division `F33f`_`[multiplexers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Multiplexer]`_`f, `F33f`_`[analog delay lines`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Analog_delay_line]`_`f and `F33f`_`[analog feedback shift registers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Analog_feedback_shift_register]`_`f. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.`:cite-ref-7[`F5bf`_`[7`#cite-note-7]`_`f]

The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking `F33f`_`[quantization error`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Quantization_error]`_`f into consideration.

>>>Digital

Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose `F33f`_`[computers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Computer]`_`f or by digital circuits such as `F33f`_`[ASICs`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ASIC]`_`f, `F33f`_`[field-programmable gate arrays`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Field-programmable_gate_array]`_`f or specialized `F33f`_`[digital signal processors`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Digital_signal_processor]`_`f. Typical arithmetical operations include `F33f`_`[fixed-point`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fixed-point_arithmetic]`_`f and `F33f`_`[floating-point`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Floating-point]`_`f, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are `F33f`_`[circular buffers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Circular_buffer]`_`f and `F33f`_`[lookup tables`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Lookup_table]`_`f. Examples of algorithms are the `F33f`_`[fast Fourier transform`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fast_Fourier_transform]`_`f (FFT), `F33f`_`[finite impulse response`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Finite_impulse_response]`_`f (FIR) filter, `F33f`_`[Infinite impulse response`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Infinite_impulse_response]`_`f (IIR) filter, and `F33f`_`[adaptive filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Adaptive_filter]`_`f such as the `F33f`_`[Wiener`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Wiener_filter]`_`f and `F33f`_`[Kalman filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Kalman_filter]`_`f.

>>>Nonlinear

Nonlinear signal processing involves the analysis and processing of signals produced from `F33f`_`[nonlinear systems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Nonlinear_system]`_`f and can be in the time, `F33f`_`[frequency`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Frequency]`_`f, or spatiotemporal domains.`:cite-ref-billings-8-0[`F5bf`_`[8`#cite-note-billings-8]`_`f]`:cite-ref-vsa-9-0[`F5bf`_`[9`#cite-note-vsa-9]`_`f] Nonlinear systems can produce highly complex behaviors including `F33f`_`[bifurcations`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bifurcation_theory]`_`f, `F33f`_`[chaos`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Chaos_theory]`_`f, `F33f`_`[harmonics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Harmonics]`_`f, and `F33f`_`[subharmonics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Subharmonics]`_`f which cannot be produced or analyzed using linear methods.

Polynomial signal processing is a type of non-linear signal processing, where `F33f`_`[polynomial`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Polynomial]`_`f systems may be interpreted as conceptually straightforward extensions of linear systems to the nonlinear case.`:cite-ref-10[`F5bf`_`[10`#cite-note-10]`_`f]

>>>Statistical

`!Statistical signal processing`! is an approach which treats signals as `F33f`_`[stochastic processes`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stochastic_process]`_`f, utilizing their `F33f`_`[statistical`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Statistical]`_`f properties to perform signal processing tasks.`:cite-ref-scharf-11-0[`F5bf`_`[11`#cite-note-scharf-11]`_`f] Statistical techniques are widely used in signal processing applications. For example, one can model the `F33f`_`[probability distribution`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Probability_distribution]`_`f of noise incurred when photographing an image, and construct techniques based on this model to `F33f`_`[reduce the noise`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Noise_reduction]`_`f in the resulting image.

>>>Graph

`!Graph signal processing`! generalizes signal processing tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph.`:cite-ref-ortega-12-0[`F5bf`_`[12`#cite-note-ortega-12]`_`f] Graph signal processing presents several key points such as sampling signal techniques,`:cite-ref-tanaka-13-0[`F5bf`_`[13`#cite-note-tanaka-13]`_`f] recovery techniques `:cite-ref-fascista-14-0[`F5bf`_`[14`#cite-note-fascista-14]`_`f] and time-varying techiques.`:cite-ref-giraldo-15-0[`F5bf`_`[15`#cite-note-giraldo-15]`_`f] Graph signal processing has been applied with success in the field of image processing, computer vision `:cite-ref-giraldo1-16-0[`F5bf`_`[16`#cite-note-giraldo1-16]`_`f] `:cite-ref-giraldo2-17-0[`F5bf`_`[17`#cite-note-giraldo2-17]`_`f] `:cite-ref-giraldo3-18-0[`F5bf`_`[18`#cite-note-giraldo3-18]`_`f] and sound anomaly detection.`:cite-ref-bouwmans1-19-0[`F5bf`_`[19`#cite-note-bouwmans1-19]`_`f]

>>Application fields

• `F33f`_`[Audio signal processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Audio_signal_processing]`_`f – for electrical signals representing sound, such as `F33f`_`[speech`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Speech_signal_processing]`_`f or music`:cite-ref-20[`F5bf`_`[20`#cite-note-20]`_`f]

• `F33f`_`[Image processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Image_processing]`_`f – in digital cameras, computers and various imaging systems

• `F33f`_`[Video processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Video_processing]`_`f – for interpreting moving pictures

• `F33f`_`[Wireless communication`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Wireless_communication]`_`f – waveform generations, demodulation, filtering, equalization

• `F33f`_`[Control systems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Control_systems]`_`f

• `F33f`_`[Array processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Array_processing]`_`f – for processing signals from arrays of sensors

• `F33f`_`[Process control`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Process_control]`_`f – a variety of signals are used, including the industry standard `F33f`_`[4-20 mA current loop`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=4-20_mA_current_loop]`_`f

• `F33f`_`[Seismology`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Seismology]`_`f

• `F33f`_`[Feature extraction`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Feature_extraction]`_`f, such as `F33f`_`[image understanding`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Image_understanding]`_`f, `F33f`_`[semantic audio`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Semantic_audio]`_`f and `F33f`_`[speech recognition`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Speech_recognition]`_`f.

• Quality improvement, such as `F33f`_`[noise reduction`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Noise_reduction]`_`f, `F33f`_`[image enhancement`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Image_enhancement]`_`f, and `F33f`_`[echo cancellation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Echo_cancellation]`_`f.

• Source coding including `F33f`_`[audio compression`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Audio_compression_(data)]`_`f, `F33f`_`[image compression`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Image_compression]`_`f, and `F33f`_`[video compression`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Video_compression]`_`f.

• `F33f`_`[Genomic`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Genomic]`_`f signal processing`:cite-ref-21[`F5bf`_`[21`#cite-note-21]`_`f]

• In `F33f`_`[geophysics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Geophysics]`_`f, signal processing is used to amplify the signal vs the noise within `F33f`_`[time-series`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Time-series]`_`f measurements of geophysical data. Processing is conducted within the `F33f`_`[time domain`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Time_domain]`_`f or `F33f`_`[frequency domain`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Frequency_domain]`_`f, or both.`:cite-ref-22[`F5bf`_`[22`#cite-note-22]`_`f]`:cite-ref-23[`F5bf`_`[23`#cite-note-23]`_`f]

In communication systems, signal processing may occur at:

• OSI layer 1 in the seven-layer `F33f`_`[OSI model`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=OSI_model]`_`f, the `F33f`_`[physical layer`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Physical_layer]`_`f (`F33f`_`[modulation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Modulation]`_`f, `F33f`_`[equalization`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Equalization_(communications)]`_`f, `F33f`_`[multiplexing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Multiplexing]`_`f, etc.);

• OSI layer 2, the `F33f`_`[data link layer`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Data_link_layer]`_`f (`F33f`_`[forward error correction`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Forward_error_correction]`_`f);

• OSI layer 6, the `F33f`_`[presentation layer`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Presentation_layer]`_`f (source coding, including `F33f`_`[analog-to-digital conversion`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Analog-to-digital_conversion]`_`f and `F33f`_`[data compression`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Data_compression]`_`f).

>>Typical devices

• `F33f`_`[Filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Filter_(signal_processing)]`_`f – for example analog (passive or active) or digital (`F33f`_`[FIR`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=FIR_filter]`_`f, `F33f`_`[IIR`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=IIR_filter]`_`f, frequency domain or `F33f`_`[stochastic filters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stochastic_filter]`_`f, etc.)

• `F33f`_`[Samplers`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sampling_(signal_processing)]`_`f and `F33f`_`[analog-to-digital converters`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Analog-to-digital_converter]`_`f for `F33f`_`[signal acquisition`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Signal_acquisition]`_`f and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof.

• `F33f`_`[Digital signal processors`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Digital_signal_processor]`_`f (DSPs)

>>Mathematical methods applied

• `F33f`_`[Differential equations`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Differential_equations]`_`f`:cite-ref-gaydecki2004-24-0[`F5bf`_`[24`#cite-note-gaydecki2004-24]`_`f] – for modeling system behavior, connecting input and output relations in linear time-invariant systems. For instance, a low-pass filter such as an `F33f`_`[RC circuit`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=RC_circuit]`_`f can be modeled as a differential equation in signal processing, which allows one to compute the continuous output signal as a function of the input or initial conditions.

• `F33f`_`[Recurrence relations`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Recurrence_relation]`_`f`:cite-ref-engelberg2008-25-0[`F5bf`_`[25`#cite-note-engelberg2008-25]`_`f]

• `F33f`_`[Transform theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Transform_theory]`_`f

• `F33f`_`[Time-frequency analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Time-frequency_analysis]`_`f – for processing non-stationary signals`:cite-ref-26[`F5bf`_`[26`#cite-note-26]`_`f]

• `F33f`_`[Linear canonical transformation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_canonical_transformation]`_`f

• `F33f`_`[Spectral estimation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Spectral_estimation]`_`f – for determining the spectral content (i.e., the distribution of power over frequency) of a set of `F33f`_`[time series`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Time_series]`_`f data points`:cite-ref-27[`F5bf`_`[27`#cite-note-27]`_`f]

• `F33f`_`[Statistical signal processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Statistical_signal_processing]`_`f – analyzing and extracting information from signals and noise based on their stochastic properties

• `F33f`_`[Linear time-invariant system`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_time-invariant_system]`_`f theory, and `F33f`_`[transform theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Transform_theory]`_`f

• `F33f`_`[Polynomial signal processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Polynomial_signal_processing]`_`f – analysis of systems which relate input and output using polynomials

• `F33f`_`[System identification`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=System_identification]`_`f`:cite-ref-billings-8-1[`F5bf`_`[8`#cite-note-billings-8]`_`f] and classification

• `F33f`_`[Calculus`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Calculus]`_`f

• `F33f`_`[Coding theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Coding_theory]`_`f

• `F33f`_`[Complex analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Complex_analysis]`_`f`:cite-ref-schreierscharf2010-28-0[`F5bf`_`[28`#cite-note-schreierscharf2010-28]`_`f]

• `F33f`_`[Vector spaces`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Vector_spaces]`_`f and `F33f`_`[Linear algebra`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_algebra]`_`f`:cite-ref-little2019-29-0[`F5bf`_`[29`#cite-note-little2019-29]`_`f]

• `F33f`_`[Functional analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Functional_analysis]`_`f`:cite-ref-damelinjr2012-30-0[`F5bf`_`[30`#cite-note-damelinjr2012-30]`_`f]

• `F33f`_`[Probability`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Probability]`_`f and `F33f`_`[stochastic processes`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stochastic_processes]`_`f`:cite-ref-scharf-11-1[`F5bf`_`[11`#cite-note-scharf-11]`_`f]

• `F33f`_`[Detection theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Detection_theory]`_`f

• `F33f`_`[Estimation theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Estimation_theory]`_`f

• `F33f`_`[Optimization`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Optimization]`_`f`:cite-ref-palomareldar2010-31-0[`F5bf`_`[31`#cite-note-palomareldar2010-31]`_`f]

• `F33f`_`[Numerical methods`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Numerical_methods]`_`f

• `F33f`_`[Data mining`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Data_mining]`_`f – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns

>>See also

• `F33f`_`[Algebraic signal processing`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Algebraic_signal_processing]`_`f

• `F33f`_`[Audio filter`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Audio_filter]`_`f

• `F33f`_`[Bounded variation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bounded_variation]`_`f

• `F33f`_`[Dynamic range compression`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Dynamic_range_compression]`_`f

• `F33f`_`[Information theory`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Information_theory]`_`f

• `F33f`_`[Least-squares spectral analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Least-squares_spectral_analysis]`_`f

• `F33f`_`[Non-local means`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Non-local_means]`_`f

• `F33f`_`[Reverberation`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Reverberation]`_`f

• `F33f`_`[Sensitivity (electronics)`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sensitivity_(electronics)]`_`f

• `F33f`_`[Similarity (signal processing)`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Similarity_(signal_processing)]`_`f

>>References

`:cite-note-1`!1.`! `F0af`_`[↑`#cite-ref-1]`_`f `:citerefsenguptasahidullah-mdsaha-goutam2016`aSengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features". `*Computers in Biology and Medicine`*. `!75`! (1): 118–129. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1016/j.compbiomed.2016.05.013. `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 27286184.

`:cite-note-2`!2.`! `F0af`_`[↑`#cite-ref-2]`_`f `:citerefalan-v-oppenheim-and-ronald-w-schafer1989`aAlan V. Oppenheim and Ronald W. Schafer (1989). `*Discrete-Time Signal Processing`*. Prentice Hall. p. 1. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-13-216771-9.

`:cite-note-3`!3.`! `F0af`_`[↑`#cite-ref-3]`_`f `:citerefoppenheim-alan-v-schafer-ronald-w-1975`aOppenheim, Alan V.; Schafer, Ronald W. (1975). `*Digital Signal Processing`*. `F33f`_`[Prentice Hall`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Prentice_Hall]`_`f. p. 5. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-13-214635-5.

`:cite-note-4`!4.`! `F0af`_`[↑`#cite-ref-4]`_`f "A Mathematical Theory of Communication – CHM Revolution". `*Computer History`*. Retrieved 2019-05-13.

`:cite-note-fifty-5`!5.`! `F0af`_`[↑`#cite-ref-fifty-5-0]`_`f `*Fifty Years of Signal Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998`* (PDF). The IEEE Signal Processing Society. 1998.

`:cite-note-6`!6.`! `F0af`_`[↑`#cite-ref-6]`_`f Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9

`:cite-note-7`!7.`! `F0af`_`[↑`#cite-ref-7]`_`f "Microwave & Millimeter-wave Circuits and Systems". Retrieved 2024-10-20.

`:cite-note-billings-8`!8.`! `F0af`_`[↑`#cite-ref-billings-8-0]`_`f `:citerefbillings2013`aBillings, S. A. (2013). `*Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains`*. Wiley. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-119-94359-4.

`:cite-note-vsa-9`!9.`! `F0af`_`[↑`#cite-ref-vsa-9-0]`_`f `:citerefslawinska-j-ourmazd-a-giannakis-d-2018`aSlawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New Approach to Signal Processing of Spatiotemporal Data". `*2018 IEEE Statistical Signal Processing Workshop (SSP)`*. IEEE Xplore. pp. 338–342. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/SSP.2018.8450704. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-5386-1571-3. `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 52153144.

`:cite-note-10`!10.`! `F0af`_`[↑`#cite-ref-10]`_`f `:citerefv-john-mathewsgiovanni-l-sicuranza2000`aV. John Mathews; Giovanni L. Sicuranza (May 2000). `*Polynomial Signal Processing`*. Wiley. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-471-03414-8.

`:cite-note-scharf-11`!11.`! `F0af`_`[↑`#cite-ref-scharf-11-0]`_`f `:citerefscharf1991`aScharf, Louis L. (1991). `*Statistical signal processing: detection, estimation, and time series analysis`*. `F33f`_`[Boston`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Boston]`_`f: `F33f`_`[Addison–Wesley`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Addison–Wesley]`_`f. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-201-19038-9. `F33f`_`[OCLC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=OCLC_(identifier)]`_`f 61160161.

`:cite-note-ortega-12`!12.`! `F0af`_`[↑`#cite-ref-ortega-12-0]`_`f `:citerefortega2022`aOrtega, A. (2022). `*Introduction to Graph Signal Processing`*. `F33f`_`[Cambridge`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cambridge]`_`f: `F33f`_`[Cambridge University Press`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cambridge_University_Press]`_`f. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9781108552349.

`:cite-note-tanaka-13`!13.`! `F0af`_`[↑`#cite-ref-tanaka-13-0]`_`f `:citereftanakaeldar2020`aTanaka, Y.; Eldar, Y. (2020). "Generalized Sampling on Graphs with Subspace and Smoothness Prior". `*IEEE Transactions on Signal Processing`*. `!68`!: 2272–2286. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:1905.04441. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2020ITSP...68.2272T. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/TSP.2020.2982325.

`:cite-note-fascista-14`!14.`! `F0af`_`[↑`#cite-ref-fascista-14-0]`_`f `:citereffascistacolucciaravazzi2024`aFascista, A.; Coluccia, A.; Ravazzi, C. (2024). "Graph Signal Reconstruction under Heterogeneous Noise via Adaptive Uncertainty-Aware Sampling and Soft Classification". `*IEEE Transactions on Signal and Information Processing over Networks`*. `!10`!: 277–293. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/TSIPN.2024.3375593.

`:cite-note-giraldo-15`!15.`! `F0af`_`[↑`#cite-ref-giraldo-15-0]`_`f `:citerefgiraldomahmoodgarcia-garciathanou2022`aGiraldo, J.; Mahmood, A.; Garcia-Garcia, B.; Thanou, D.; Bouwmans, T. (March 2022). "Reconstruction of Time-varying Graph Signals via Sobolev Smoothness". `*IEEE Transactions on Signal and Information Processing over Networks`*. `!8`!: 201–214. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:2207.06439. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/TSIPN.2022.3156886.

`:cite-note-giraldo1-16`!16.`! `F0af`_`[↑`#cite-ref-giraldo1-16-0]`_`f `:citerefgiraldobouwmans2020`aGiraldo, J.; Bouwmans, T. (October 2020). "Semi-Supervised Background Subtraction of Unseen Videos: Minimization of the Total Variation of Graph Signals". `*2020 IEEE International Conference on Image Processing (ICIP)`*. pp. 3224–3228. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/ICIP40778.2020.9190887. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-7281-6395-6.

`:cite-note-giraldo2-17`!17.`! `F0af`_`[↑`#cite-ref-giraldo2-17-0]`_`f `:citerefgiraldobouwmans2020`aGiraldo, J.; Bouwmans, T. (2020). "GraphBGS: Background Subtraction via Recovery of Graph Signals". `*2020 25th International Conference on Pattern Recognition (ICPR)`*. pp. 6881–6888. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:2001.06404. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/ICPR48806.2021.9412999. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-7281-8808-9.

`:cite-note-giraldo3-18`!18.`! `F0af`_`[↑`#cite-ref-giraldo3-18-0]`_`f `:citerefgiraldojavedsultanajung2021`aGiraldo, J.; Javed, S.; Sultana, M.; Jung, S.; Bouwmans, T. (February 2021). "The Emerging Field of Graph Signal Processing for Moving Object Segmentation". `*Frontiers of Computer Vision`*. Communications in Computer and Information Science. Vol. 1405. pp. 31–45. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1007/978-3-030-81638-4_3. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-3-030-81637-7.

`:cite-note-bouwmans1-19`!19.`! `F0af`_`[↑`#cite-ref-bouwmans1-19-0]`_`f `:citerefmnasrigiraldobouwmans2024`aMnasri, Z.; Giraldo, H.; Bouwmans, T. (2024). "Anomalous Sound Detection for Road Surveillance based on Graph Signal Processing". `*European Conference on Signal Processing, EUSIPCO 2024`*: 161–165. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.23919/EUSIPCO63174.2024.10715291. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-9-4645-9361-7.

`:cite-note-20`!20.`! `F0af`_`[↑`#cite-ref-20]`_`f `:citerefsarangisahidullah-mdsaha-goutam2020`aSarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification". `*Digital Signal Processing`*. `!104`!: 102795. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:2007.10729. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2020DSP...10402795S. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1016/j.dsp.2020.102795. `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 220665533.

`:cite-note-21`!21.`! `F0af`_`[↑`#cite-ref-21]`_`f `:citerefanastassiou2001`aAnastassiou, D. (2001). "Genomic signal processing". `*IEEE Signal Processing Magazine`*. `!18`! (4). IEEE: 8–20. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2001ISPM...18....8A. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1109/79.939833.

`:cite-note-22`!22.`! `F0af`_`[↑`#cite-ref-22]`_`f `:citereftelfordgeldartsheriff1990`aTelford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990). `*Applied geophysics`*. `F33f`_`[Cambridge University Press`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cambridge_University_Press]`_`f. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-521-33938-4.

`:cite-note-23`!23.`! `F0af`_`[↑`#cite-ref-23]`_`f `:citerefreynolds2011`aReynolds, John M. (2011). `*An Introduction to Applied and Environmental Geophysics`*. `F33f`_`[Wiley-Blackwell`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Wiley-Blackwell]`_`f. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-471-48535-3.

`:cite-note-gaydecki2004-24`!24.`! `F0af`_`[↑`#cite-ref-gaydecki2004-24-0]`_`f `:citerefpatrick-gaydecki2004`aPatrick Gaydecki (2004). `*Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design`*. IET. pp. 40–. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-85296-431-6.

`:cite-note-engelberg2008-25`!25.`! `F0af`_`[↑`#cite-ref-engelberg2008-25-0]`_`f `:citerefshlomo-engelberg2008`aShlomo Engelberg (8 January 2008). `*Digital Signal Processing: An Experimental Approach`*. Springer Science & Business Media. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-84800-119-0.

`:cite-note-26`!26.`! `F0af`_`[↑`#cite-ref-26]`_`f `:citerefboashash-boualem2003`aBoashash, Boualem, ed. (2003). `*Time frequency signal analysis and processing a comprehensive reference`* (1 ed.). Amsterdam: Elsevier. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-08-044335-4.

`:cite-note-27`!27.`! `F0af`_`[↑`#cite-ref-27]`_`f `:citerefstoicamoses2005`aStoica, Petre; Moses, Randolph (2005). `*Spectral Analysis of Signals`* (PDF). NJ: Prentice Hall.

`:cite-note-schreierscharf2010-28`!28.`! `F0af`_`[↑`#cite-ref-schreierscharf2010-28-0]`_`f `:citerefpeter-j-schreierlouis-l-scharf2010`aPeter J. Schreier; Louis L. Scharf (4 February 2010). `*Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals`*. Cambridge University Press. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-139-48762-7.

`:cite-note-little2019-29`!29.`! `F0af`_`[↑`#cite-ref-little2019-29-0]`_`f `:citerefmax-a-little2019`aMax A. Little (13 August 2019). `*Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics`*. OUP Oxford. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-19-102431-3.

`:cite-note-damelinjr2012-30`!30.`! `F0af`_`[↑`#cite-ref-damelinjr2012-30-0]`_`f `:citerefsteven-b-damelinwillard-miller-jr2012`aSteven B. Damelin; Willard Miller, Jr (2012). `*The Mathematics of Signal Processing`*. Cambridge University Press. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-1-107-01322-3.

`:cite-note-palomareldar2010-31`!31.`! `F0af`_`[↑`#cite-ref-palomareldar2010-31-0]`_`f `:citerefdaniel-p-palomaryonina-c-eldar2010`aDaniel P. Palomar; Yonina C. Eldar (2010). `*Convex Optimization in Signal Processing and Communications`*. Cambridge University Press. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-521-76222-9.

>>Further reading

• `:citerefbyrne2014`aByrne, Charles (2014). `*Signal Processing: A Mathematical Approach`*. `F33f`_`[Taylor & Francis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Taylor_&_Francis]`_`f. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1201/b17672. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9780429158711.

• `:citerefp-stoica2005`aP Stoica, R Moses (2005). `*Spectral Analysis of Signals`* (PDF). NJ: Prentice Hall.

• `:citerefpapoulis1991`aPapoulis, Athanasios (1991). `*Probability, Random Variables, and Stochastic Processes`* (third ed.). McGraw-Hill. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-07-100870-5.

• Kainam Thomas Wong [1]: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.

• `F33f`_`[Ali H. Sayed`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Ali_H._Sayed]`_`f, Adaptive Filters, Wiley, NJ, 2008, `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-470-25388-5.

• `F33f`_`[Thomas Kailath`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Thomas_Kailath]`_`f, `F33f`_`[Ali H. Sayed`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Ali_H._Sayed]`_`f, and `F33f`_`[Babak Hassibi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Babak_Hassibi]`_`f, Linear Estimation, Prentice-Hall, NJ, 2000, `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 978-0-13-022464-4.

>>External links

• Signal Processing for Communications – free online textbook by Paolo Prandoni and Martin Vetterli (2008)

• Scientists and Engineers Guide to Digital Signal Processing – free online textbook by Stephen Smith

• Julius O. Smith III: Spectral Audio Signal Processing – free online textbook

• Graph Signal Processing Website – free online website by Thierry Bouwmans (2025)

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