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Spectral band

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Spectral bands are regions of a given spectrum, having a specific range of wavelengths or frequencies. Most often, it refers to electromagnetic bands, regions of the electromagnetic spectrum.^[1] More generally, spectral bands may also be means in the spectra of other types of signals, e.g., noise spectrum.

A frequency band is an interval in the frequency domain, limited by a lower frequency and an upper frequency. For example, it may refer to a radio band, such as wireless communication standards set by the International Telecommunication Union.^[2]

In nuclear physics

[edit]

In nuclear physics, spectral bands refer to the electromagnetic emission of polyatomic systems, including condensed materials, large molecules, etc. Each spectral line corresponds to the difference in two energy levels of an atom. In molecules, these levels can split. When the number of atoms is large, one gets a continuum of energy levels, the so-called spectral bands. They are often labeled in the same way as the monatomic lines.

The bands may overlap. In general, the energy spectrum can be given by a density function, describing the number of energy levels of the quantum system for a given interval. Spectral bands have constant density, and when the bands overlap, the corresponding densities are added.

Band spectra is the name given to a group of lines that are closely spaced and arranged in a regular sequence that appears to be a band. It is a colored band, separated by dark spaces on the two sides and arranged in a regular sequence. In one band, there are various sharp and wider color lines, that are closer on one side and wider on other. The intensity in each band falls off from definite limits and indistinct on the other side. In complete band spectra, there is a number lines in a band.

This spectra is produced when the emitting substance is in the molecular state. Therefore, they are also called molecular spectra. It is emitted by a molecule in vacuum tube, C-arc core with metallic salt. The band spectrum is the combination of many different spectral lines, resulting from molecular vibrational, rotational, and electronic transition.

Spectroscopy studies spectral bands for astronomy and other purposes.

Other applications

[edit]

Many systems are characterized by the spectral band to which they respond. For example:

Musical instruments produce different ranges of notes within the hearing range.
The electromagnetic spectrum can be divided into many different ranges such as visible light, infrared or ultraviolet radiation, radio waves, X-rays and so on, and each of these ranges can in turn be divided into smaller ranges.
A radio communications signal must occupy a range of frequencies carrying most of its energy, called its bandwidth. A frequency band may represent one communication channel or be subdivided into many. Allocation of radio frequency ranges to different uses is a major function of radio spectrum allocation.

References

[edit]

^ Mehta, Akul (25 August 2011). "Introduction to the Electromagnetic Spectrum and Spectroscopy". Pharmaxchange.info. Retrieved 2011-11-08.
^ "An Overview of Frequency Bands and Their Applications". resources.pcb.cadence.com. 3 November 2022. Retrieved 2023-04-18.

Revisions and contributors Edit on Wikipedia Read on Wikipedia

View on Grokipedia

from Grokipedia

A spectral band is a well-defined, continuous interval or range of wavelengths or frequencies within the electromagnetic spectrum, typically used to isolate and measure specific portions of electromagnetic radiation for analysis in scientific and technical applications.^[1] These bands are characterized by a central wavelength and a bandwidth, enabling precise segmentation of the spectrum for various purposes.^[2] In remote sensing and Earth observation, spectral bands form the basis of multispectral and hyperspectral imaging systems, where sensors capture reflected or emitted energy from Earth's surface in discrete wavelength intervals to identify materials, vegetation health, and environmental changes based on unique spectral signatures.^[3] For instance, the Landsat 8 satellite employs 11 spectral bands across the visible, near-infrared, shortwave infrared, and thermal infrared regions, including Band 1 (coastal aerosol: 0.43–0.45 µm at 30 m resolution) for atmospheric correction and Band 5 (near-infrared: 0.85–0.88 µm at 30 m resolution) for vegetation monitoring.^[4] Band 4 (red: 0.64–0.67 µm) and Band 3 (green: 0.53–0.59 µm) contribute to natural color composites, while thermal bands like Band 10 (10.60–11.19 µm at 100 m resolution) assess surface temperature.^[4] These bands allow for applications such as land cover classification, crop monitoring, and disaster assessment by exploiting differences in how objects reflect or absorb radiation at specific wavelengths.^[5] In spectroscopy, spectral bands refer to regions where absorption, emission, or transmission of light occurs, revealing molecular and atomic structures through characteristic patterns like absorption bands in infrared spectra.^[6] Instruments in this field use narrow spectral bands to resolve fine details, such as vibrational transitions in molecules, aiding in chemical identification and material characterization.^[7] In astronomy and radio communications, spectral bands denote designated frequency ranges, such as the S-band (2–4 GHz) used for satellite telemetry or X-band (8–12 GHz) for radar observations, facilitating interference-free signal transmission and celestial object studies.^[8] Overall, the design and selection of spectral bands are critical for optimizing resolution, sensitivity, and data utility across these domains, with ongoing advancements in sensor technology enabling finer bandwidths for more detailed spectral analysis.^[3]

Fundamentals

Definition

A spectral band is a contiguous range of wavelengths, frequencies, or wavenumbers within an electromagnetic spectrum where particular physical processes, such as absorption or emission of radiation, take place or are observed.^[9] These bands represent regions of enhanced or diminished intensity due to interactions between matter and electromagnetic radiation, commonly observed in spectroscopic studies of atoms, molecules, and materials.^[10] Spectral bands are typically denoted using units of wavelength (e.g., nanometers [nm] or micrometers [μm]), frequency (e.g., hertz [Hz] or terahertz [THz]), or wavenumber (e.g., inverse centimeters [cm⁻¹]).^[11] For instance, the visible light band spans approximately 400–700 nm, corresponding to frequencies around 430–750 THz and wavenumbers of about 14,000–25,000 cm⁻¹.^[12] Unlike discrete spectral lines, which appear as narrow peaks from individual quantum transitions in atomic spectra, spectral bands are broader features arising from the overlap of numerous closely spaced lines, often due to rotational and vibrational energy levels in molecular systems.^[13] This broadening distinguishes bands as extended regions rather than isolated features, reflecting the complexity of multi-level quantum interactions.^[10] The concept of spectral bands originated in early 20th-century spectroscopy, as researchers applied emerging quantum theory to interpret molecular emission and absorption patterns. Building on Niels Bohr's 1913 atomic model, which explained discrete line spectra in hydrogen,^[14] scientists extended these ideas to molecular systems, developing the quantum theory of band spectra by the 1920s.^[15] This foundational work marked a shift toward understanding continuous spectral regions in polyatomic structures.

Characteristics

Spectral bands exhibit several fundamental physical properties that enable their quantification and analysis in spectroscopic measurements. The intensity of a band, which reflects the strength of the underlying transition, can be assessed either as the peak height—the maximum absorbance or transmittance deviation—or as the integrated area under the curve, providing a measure of the total transition probability. The central position of the band is defined by its center frequency or wavelength, corresponding to the energy difference between quantum states involved in the transition. Band width is typically characterized by the full width at half maximum (FWHM), representing the range over which the intensity drops to half its peak value, often on the order of picometers to nanometers depending on the system. Asymmetry describes deviations from a symmetric profile, arising from factors like overlapping transitions or instrumental effects, and is quantified by ratios such as the skewness parameter or tail-to-peak intensity ratios. The observed characteristics of spectral bands are significantly influenced by the resolution of the measuring instrument. Instrumental resolution determines the ability to distinguish fine spectral features, with poorer resolution leading to apparent broadening and merging of bands that would otherwise appear distinct. The resolving power

R

is formally defined as

R = \frac{\lambda}{\Delta \lambda}

, where

\lambda

is the central wavelength and

\Delta \lambda

is the minimum resolvable wavelength separation, typically achieving values from hundreds to tens of thousands in modern spectrometers. The distribution and intensity of spectral bands are governed by quantum mechanical principles, particularly the transition probabilities between energy levels. In atomic and molecular systems, the oscillator strength

f

, a dimensionless quantity ranging from near zero for forbidden transitions to around 1 for fully allowed ones, directly scales with the band's integrated intensity and encapsulates the likelihood of photon absorption or emission. Environmental conditions play a crucial role in modifying band properties through broadening mechanisms. Temperature induces Doppler broadening from the thermal motion of particles, resulting in a Gaussian profile with FWHM given by

\Delta \nu_D = \frac{\nu_0}{c} \sqrt{\frac{8 k T \ln 2}{m}}

ΔνD=cν0m8kTln2

, where $\nu_0$ is the central frequency, $c$ is the speed of light, $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is the mass of the emitting species; this effect increases with higher temperatures and lighter particles. Pressure contributes to collisional or Lorentzian broadening via interactions that shorten excited-state lifetimes, while the surrounding medium can introduce additional shifts or widths through refractive index variations or solvent effects. These influences are particularly relevant in contexts like absorption and emission spectroscopy, where band profiles inform about molecular environments.

In Spectroscopy and Optics

Absorption and Emission Bands

Absorption bands occur in regions of the electromagnetic spectrum where molecules or atoms absorb photons, leading to excitation of electrons from ground to higher energy states or to vibrational modes within molecules. This absorption is characteristic of specific substances and provides insight into their electronic and vibrational structures. For instance, in ultraviolet-visible (UV-Vis) spectroscopy, organic dyes like chlorophyll exhibit distinct absorption bands; chlorophyll a shows strong absorptions at approximately 430 nm (blue) and 662 nm (red), corresponding to π → π* transitions in its porphyrin ring.^[16]^[17] Emission bands arise when excited species relax to lower energy states, releasing photons in processes such as fluorescence (rapid emission from singlet states) or phosphorescence (delayed emission from triplet states). These bands typically appear at longer wavelengths than absorption bands due to energy loss through vibrational relaxation. A key feature is the Stokes shift, defined as the difference between the absorption and emission maxima, which for fluorescent dyes like fluorescein is around 20-30 nm and arises from reorganization of the solvent shell around the excited molecule.^[18]^[19] Quantitative analysis of absorption bands relies on the Beer-Lambert law, which states that the absorbance

A

of a solution is directly proportional to the concentration

c

of the absorbing species, the molar absorptivity

\epsilon

(a constant specific to the substance and wavelength), and the path length

l

through the sample:

A = \epsilon c l

This law enables determination of unknown concentrations in analytical chemistry, such as measuring dye concentrations in solutions, provided the solution is dilute to avoid deviations from linearity.^[20] In infrared (IR) spectroscopy, absorption bands often involve coupled rotational-vibrational transitions, forming complex band envelopes. For diatomic or linear polyatomic molecules, these spectra display P, Q, and R branches: the P branch corresponds to transitions where the rotational quantum number

J

decreases (

\Delta J = -1

), appearing at lower wavenumbers; the Q branch (

\Delta J = 0

) is sometimes present in perpendicular transitions of polyatomics, forming a central peak; and the R branch (

\Delta J = +1

) appears at higher wavenumbers. These branches envelope the pure vibrational frequency, with spacing influenced by the rotational constant

B

, as seen in the HCl fundamental vibration around 2886 cm⁻¹.^[21]^[22]

Band Shapes and Widths

Spectral bands in spectroscopy often exhibit characteristic shapes determined by underlying physical processes, with the most common profiles being Gaussian, Lorentzian, and Voigt. The Gaussian profile arises primarily from Doppler broadening due to the thermal motion of emitting or absorbing particles, following a Maxwell-Boltzmann velocity distribution. Its intensity as a function of frequency detuning

\Delta \nu = \nu - \nu_0

is given by

I(\Delta \nu) = I_0 \exp\left(-\frac{(\Delta \nu)^2}{2\sigma^2}\right)

, where

\sigma

is the standard deviation, and the full width at half maximum (FWHM) is

\Delta \nu = \frac{2\nu_0}{c} \sqrt{2 \ln 2 \frac{kT}{m}}

Δν=c2ν02ln2mkT

, with $\nu_0$ the central frequency, $c$ the speed of light, $k$ Boltzmann's constant, $T$ temperature, and $m$ the particle mass.^[23]^[24] In contrast, the Lorentzian profile results from natural or lifetime broadening, where the finite lifetime $\tau$ of excited states leads to an uncertainty in energy levels. The profile is $I(\Delta \nu) = I_0 \frac{(\Delta \nu_{1/2}/2)^2}{(\Delta \nu)^2 + (\Delta \nu_{1/2}/2)^2}$ , with FWHM $\Delta \nu = \frac{1}{2\pi \tau}$ , derived from the Fourier transform of an exponentially decaying wavefunction.^[25]^[26] Pressure or collisional broadening also produces Lorentzian shapes by shortening the effective lifetime through intermolecular interactions.^[27] The Voigt profile represents the convolution of Gaussian and Lorentzian components, accounting for combined Doppler and lifetime/pressure effects, and is prevalent in real spectra under atmospheric or laboratory conditions. It lacks a simple analytical form but can be approximated or computed numerically, with the overall FWHM depending on the relative contributions of the two profiles.^[26]^[28] Broadening mechanisms fundamentally shape these profiles. Natural broadening stems from the Heisenberg uncertainty principle, $\Delta E \Delta t \geq \hbar/2$ , where the energy uncertainty $\Delta E = h \Delta \nu$ arises from the finite excited-state lifetime $\Delta t = \tau$ .^[27] Pressure broadening occurs via collisions that interrupt wavefunction coherence, scaling with gas density and leading to Lorentzian wings.^[29] Broadening is classified as homogeneous if all molecules experience the same shift and width (e.g., natural or collisional), resulting in uniform Lorentzian profiles, or inhomogeneous if subpopulations differ (e.g., Doppler due to velocity variations), yielding Gaussian envelopes.^[29]^[30] To analyze overlapping bands, deconvolution techniques separate individual profiles from composite spectra. Least-squares fitting minimizes the difference between observed data and a model sum of profiles (e.g., Voigt functions), iteratively adjusting parameters like central frequency, width, and amplitude while accounting for noise.^[31]^[32] This method is widely used in high-resolution spectroscopy to resolve subtle features.^[33] In infrared (IR) spectroscopy, vibrational band envelopes exemplify these concepts, arising from rovibrational transitions where rotational sublevels broaden the fundamental vibrational mode into a P-, Q-, and R-branch structure. For diatomic molecules like HCl, the envelope approximates a Gaussian or Voigt shape at room temperature due to dominant Doppler and pressure effects, with the central Q-branch intensity modulated by the rotational population distribution.^[34]^[35]

In Nuclear Physics

Energy Level Groupings

In nuclear physics, spectral bands manifest as clusters of closely spaced energy levels in atomic nuclei, where states with similar quantum configurations have excitation energies differing by keV to MeV scales. These groupings typically arise from shell model orbitals filled in specific ways, leading to collective behaviors in deformed nuclei, such as rotational sequences where angular momentum projections align to form coherent structures. Such bands form through the interplay of single-particle motions and collective excitations, often in nuclei distant from closed shells. In even-even nuclei, the ground-state rotational band exemplifies this, comprising levels with even spin values (I = 0^+, 2^+, 4^+, ...) built on a deformed intrinsic state. The energies follow the rigid rotor approximation, given by

E_I = \frac{\hbar^2}{2 \mathcal{I}} I(I+1),

where

\mathcal{I}

is the nuclear moment of inertia, reflecting the deformed charge distribution; for instance, in ^{154}Sm, the 2^+ state lies at 82 keV, with subsequent levels scaling accordingly to reveal the band's characteristic I(I+1) progression. This arises from nucleons in high-j orbitals contributing to deformation, as predicted by the unified model combining shell structure with collective rotation. These bands are observed primarily via gamma-ray spectroscopy, where de-excitation cascades produce sequences of stretched E2 transitions mapping the level spacings. In thermal neutron capture reactions like (n,\gamma), compound nuclei decay through such cascades, yielding spectra that delineate band structures; early measurements at facilities like the Oak Ridge High Flux Isotope Reactor (HFIR) resolved these in rare-earth isotopes, confirming rotational patterns up to I ≈ 10\hbar. The identification of these energy level groupings traces to the mid-1950s, evolving from the independent shell model proposals by Maria Goeppert Mayer and J. Hans D. Jensen in 1949, which explained magic numbers and single-particle levels, to the collective rotational framework advanced by Aage Bohr, Ben R. Mottelson, and Leo James Rainwater. Their unified model, integrating deformation with shell effects, was experimentally validated through quadrupole moment and transition rate studies, earning the 1975 Nobel Prize in Physics.^[36]

Quantum Number Correlations

In deformed nuclei, rotational spectral bands are characterized by specific quantum numbers that correlate the angular momentum states within the band. The total spin quantum number

I

describes the magnitude of the nuclear angular momentum, while the parity

\pi

(+ or -) indicates the behavior of the wave function under spatial inversion. The projection quantum number

K

, which represents the component of angular momentum along the intrinsic symmetry axis of the deformed nucleus, serves as a primary label for band classification and distinguishes bands with the same

I

but different configurations. These quantum numbers arise from the collective rotational model, where the nucleus behaves as a rigid or irrotational body, and their correlations ensure that band members share the same

K^\pi

at the bandhead, with

I

increasing in steps of 1 or 2.^[37] Bands are classified according to

K

values, reflecting different intrinsic deformations or vibrational excitations. The ground-state band typically has

K = 0^+

, corresponding to the lowest-energy configuration with axial symmetry. Excited

K = 0^+

bands, known as beta bands, arise from quadrupole oscillations along the symmetry axis, while gamma bands feature

K = 2^+

and stem from transverse quadrupole vibrations that break the axial symmetry. These classifications highlight how

K

correlates with the band's intrinsic structure, with parity

\pi

often conserved within the band due to the even nature of collective modes.^[38] Transitions within and between bands obey selection rules derived from the multipole expansion of the electromagnetic interaction. For intraband electric quadrupole (E2) transitions, which dominate the decay patterns, the change in spin is

\Delta I = 0, \pm 1, \pm 2

(excluding

0 \to 0

), with no parity change, but consecutive intraband steps are stretched

\Delta I = 2

. Interband E2 transitions, such as those linking gamma to ground bands, favor

\Delta I = 0, \pm 1

due to the

\Delta K = 2

requirement. The rotational character is further confirmed by the moment of inertia

\mathcal{I}

, which signatures the band through the energy formula

E(I) = \frac{\hbar^2}{2 \mathcal{I}} \left[ I(I+1) - K^2 \right] + E_0,

where

E_0

is the bandhead energy; variations in

\mathcal{I}

reflect the nuclear deformation and distinguish rotational from vibrational sequences.^[39]^[40] Isotopic variations in these correlations arise from changes in neutron and proton numbers, which alter the nuclear deformation and thus shift band positions and

\mathcal{I}

values. In the rare-earth region, for instance, the dysprosium isotopes near

A = 160

exhibit systematic evolution: in

^{160}\mathrm{Dy}

(with 94 neutrons and 66 protons), the ground and gamma bands display pronounced rotational features with

\mathcal{I}

increasing toward midshell due to enhanced quadrupole deformation from added neutrons filling deformed orbitals. Neighboring isotopes like

^{158}\mathrm{Dy}

and

^{162}\mathrm{Dy}

show contracted band spacings and altered

K

assignments as the neutron excess modifies the potential energy surface.^[41]^[42] Experimental identification of these bands and their quantum number assignments relies on reactions that selectively populate specific states. Coulomb excitation, using heavy-ion beams at sub-barrier energies, excites low-spin members of rotational bands via virtual photon absorption, allowing measurement of

B(\mathrm{E2})

values to confirm

K^\pi

and

\mathcal{I}

. Transfer reactions, such as one-nucleon pickup or stripping with light ions, populate higher-spin states and enable angular distribution analysis to determine

I

and parity through Doppler-shift attenuation. These methods have been pivotal in mapping band structures in deformed nuclei, linking observed spectra to theoretical predictions without significant fragmentation.^[43]^[44]

In Remote Sensing and Imaging

Multispectral Applications

Multispectral imaging in remote sensing involves capturing electromagnetic radiation in a limited number of discrete, predefined spectral bands, typically ranging from 3 to 15 narrow wavelength intervals, to enable the discrimination of materials based on their unique reflectance or emission signatures across these bands. This approach contrasts with panchromatic imaging by providing enhanced spectral resolution, allowing for the separation of features that appear similar in broadband visible light but differ in specific wavelengths. For instance, the Landsat program's Multispectral Scanner (MSS), operational since 1972, utilized four spectral bands in the visible and near-infrared: green (0.50–0.60 μm), red (0.60–0.70 μm), near-infrared 1 (0.70–0.80 μm), and near-infrared 2 (0.80–1.10 μm), all at approximately 60 m resolution, facilitating detailed surface analysis over large areas. Later Landsat sensors, such as the Thematic Mapper, added bands including blue (0.45–0.52 μm) and shortwave infrared up to 2.35 μm.^[45] Key applications of multispectral imaging include land cover classification, where bands in the visible and near-infrared spectrum help map urban expansion, forests, and water bodies by leveraging differences in albedo and vegetation reflectance. In agriculture, the Normalized Difference Vegetation Index (NDVI), calculated as NDVI = (NIR - Red) / (NIR + Red), quantifies vegetation health and biomass by exploiting the strong chlorophyll absorption in the red band (around 0.65 μm) and high reflectance in the near-infrared band (around 0.85 μm), with values typically ranging from -1 to 1 to indicate barren to dense vegetation. Mineral mapping benefits from shortwave infrared bands (e.g., 1.55-1.75 μm and 2.08-2.35 μm in Landsat), which reveal diagnostic absorption features of minerals like kaolinite and montmorillonite, aiding in resource exploration and environmental monitoring. Prominent sensors exemplify these capabilities: the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA's Terra and Aqua satellites operates with 36 spectral bands from 0.4 to 14.4 μm, offering spatial resolutions from 250 m to 1 km, which supports global-scale applications like daily vegetation monitoring and fire detection. Advantages over panchromatic systems are evident in scenarios like soil type discrimination, where shortwave infrared reflectance distinguishes clay-rich soils from sandy ones due to hydroxyl group absorptions around 2.2 μm, improving classification accuracy in thematic mapping.

Hyperspectral Applications

Hyperspectral imaging acquires data across more than 100 contiguous spectral bands, each typically narrower than 10 nm, spanning wavelengths from approximately 400 to 2500 nm to capture detailed spectral signatures of materials.^[46] This fine resolution enables the discrimination of subtle differences in reflectance, far surpassing multispectral approaches with coarser bands. A seminal example is the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), developed by NASA's Jet Propulsion Laboratory, which operates with 224 bands over 400–2500 nm for Earth remote sensing applications.^[47] Spaceborne hyperspectral sensors include the Italian Space Agency's PRISMA (launched 2019, 239 bands) and Germany's EnMAP (launched 2022, 242 bands), enabling global monitoring of environmental changes and resource mapping; recent commercial satellites like Planet's Tanager-1 (launched August 2024, over 400 bands) further enhance data accessibility as of 2025.^[48] Hyperspectral sensors commonly employ two scanning mechanisms: pushbroom systems, which image entire lines simultaneously as the platform moves forward, providing efficient coverage and stronger signal per pixel; and whiskbroom systems, which use a rotating mirror to scan points sequentially across a line, offering flexibility but potentially lower signal-to-noise ratios due to shorter dwell times.^[49] In precision agriculture, hyperspectral imaging detects crop stress through minute changes in plant reflectance spectra, such as shifts in chlorophyll absorption around 680 nm or water content indicators near 1450 nm, allowing early intervention to optimize yields and resource use.^[50] For environmental monitoring, it identifies oil spills by matching unique hydrocarbon spectral signatures in the shortwave infrared (e.g., absorption features at 1720–1750 nm), enabling rapid assessment of spill extent and composition from airborne or satellite platforms.^[51] In defense applications, hyperspectral data reveals camouflaged targets by exploiting mismatches between artificial materials and natural backgrounds across numerous bands, where multispectral methods might fail due to limited resolution.^[52] Data processing in hyperspectral analysis often begins with spectral unmixing to decompose mixed pixels into constituent endmembers, based on the linear mixing model where the observed spectrum

\mathbf{r}

is approximated as

\mathbf{r} = \sum_{i=1}^{p} f_i \mathbf{s}_i + \mathbf{n},

with

f_i

as abundance fractions (summing to 1),

\mathbf{s}_i

as endmember spectra, and

\mathbf{n}

as noise; this model assumes sub-pixel mixing without significant nonlinear interactions.^[53] Dimensionality reduction techniques like principal component analysis (PCA) then address the high redundancy in hundreds of bands by projecting data onto fewer orthogonal components that retain most variance, facilitating classification and visualization without substantial information loss.^[54] Key challenges include managing massive data volumes, often reaching gigabytes for a single scene due to the hundreds of bands and high spatial resolutions, which demand efficient compression and storage strategies.^[50] Atmospheric correction is equally critical to remove scattering and absorption effects from gases like water vapor and aerosols; the MODTRAN radiative transfer model simulates these influences to convert at-sensor radiance to surface reflectance, though it requires accurate input parameters such as visibility and altitude for reliable results.^[55]

Other Technical Applications

Audio Signal Processing

In audio signal processing, the audible frequency spectrum is typically divided into low-frequency and high-frequency bands to facilitate efficient compression, particularly at low bitrates where full-bandwidth encoding is impractical. For instance, the low band often covers frequencies up to approximately 8 kHz, while the high band extends from 8 kHz to 16 kHz or higher, depending on the application. Spectral band replication (SBR) addresses the limitations of narrowband coding by reconstructing the high-frequency content from the low-band signal using harmonic redundancy, thereby enhancing perceived audio quality without transmitting the full high-band spectrum.^[56]^[57] The SBR mechanism employs parametric coding, where the encoder analyzes the high-band envelope and transmits a compact set of parameters—such as spectral envelope shape, noise levels, and coupling information—alongside the core low-band waveform data. At the decoder, high frequencies are synthesized through transposition techniques, such as shifting portions of the low-band spectrum upward by an octave or using patching to copy and adapt spectral segments, followed by application of the transmitted envelope to match the original timbre. This approach leverages the perceptual similarity between low and high harmonics in audio signals, enabling efficient reconstruction with minimal additional bitrate overhead of about 2-4 kb/s. SBR is integrated as an enhancement layer in codecs like Advanced Audio Coding (AAC) and High-Efficiency AAC (HE-AAC), where the core coder handles the low band and SBR operates post-decoding.^[56]^[58] Applications of SBR are prominent in low-bitrate scenarios, such as streaming audio at 24 kb/s for speech enhancement or 64 kb/s for stereo music, where it extends bandwidth to achieve near-full-range quality suitable for mobile devices and digital broadcasting. In speech processing, SBR improves intelligibility by restoring high-frequency consonants, while for music, it preserves harmonic richness in compressed streams. Perceptual quality is commonly evaluated using the Perceptual Evaluation of Audio Quality (PEAQ) metric, standardized in ITU-R BS.1387, which correlates objective scores with subjective listening tests and shows improvements for SBR-enhanced signals compared to non-extended narrowband audio at equivalent bitrates.^[59]^[56] SBR was developed in the late 1990s by Coding Technologies, a Swedish firm founded in 1997, as a novel bandwidth extension method to boost compression efficiency in perceptual audio coders. It gained prominence through products like mp3PRO and was standardized in 2003 as part of MPEG-4 Audio Amendment 1, enabling its adoption in HE-AAC for applications like Digital Radio Mondiale (DRM).^[56]^[58]

Telecommunications and Radar

In telecommunications and radar systems, spectral bands refer to designated portions of the radio frequency (RF) spectrum allocated for specific uses to ensure efficient signal transmission, minimal interference, and reliable operation. The International Telecommunication Union (ITU) classifies these bands using letter designations that correspond to frequency ranges, facilitating global standardization. For instance, the L-band spans 1 to 2 GHz and is commonly used for global positioning system (GPS) signals due to its ability to penetrate foliage and provide long-range navigation accuracy.^[60] Similarly, the S-band covers 2 to 4 GHz and supports weather radar applications, where its moderate wavelength enables detection of precipitation and storm patterns over extended areas.^[61] The X-band, ranging from 8 to 12 GHz, is widely employed in radar for air traffic control, offering high-resolution imaging for precise aircraft tracking and collision avoidance in terminal areas.^[61] In higher frequencies, the Ka-band (26.5 to 40 GHz) plays a key role in 5G wireless communications, enabling high-data-rate backhaul links and mobile services through its wide bandwidth availability.^[62] These allocations prevent spectral overlap, with bandwidth assigned based on application needs—such as narrow bands for radar Doppler processing in the X-band to measure velocity shifts in air traffic scenarios, or broader allocations in Ka-band to support the high throughput demands of modern wireless networks.^[61] A critical aspect of spectral band performance in these systems is the link budget, which quantifies the received signal power to ensure reliable communication. The Friis transmission equation models this in free space as:

P_r = P_t G_t G_r \left( \frac{\lambda}{4\pi d} \right)^2

where

P_r

is the received power,

P_t

is the transmitted power,

G_t

and

G_r

are the transmitter and receiver antenna gains,

\lambda

is the wavelength, and

d

is the distance. This equation highlights how higher-frequency bands like Ka-band experience greater free-space path loss due to shorter wavelengths, necessitating higher gains or shorter ranges for viable links. Propagation characteristics vary significantly across bands, influencing system design. Lower bands like L- and S-band exhibit lower free-space path loss, supporting robust long-distance propagation for GPS and weather monitoring even in adverse conditions. In contrast, millimeter-wave (mmWave) bands above 30 GHz, such as those explored for 6G extensions beyond Ka-band, face challenges from increased atmospheric absorption and path loss, which can exceed 20 dB/km in rainy conditions, limiting range but enabling ultra-high data rates through massive bandwidths.^[63] These properties drive innovations like beamforming to mitigate attenuation in high-band radar and telecom applications.^[63] Regulatory frameworks underpin spectral band management to avoid interference and promote equitable access. The U.S. Radio Act of 1927 established the Federal Radio Commission (predecessor to the FCC) to allocate frequencies amid growing broadcast demands, marking the start of formalized spectrum governance.^[64] Today, the FCC and ITU oversee auctions for commercial bands, such as those in Ka-band for 5G, generating billions in revenue while enforcing technical standards for power limits and emission masks.^[65] This international coordination ensures bands like S- and X-band remain dedicated to critical radar uses, balancing innovation with public safety.^[64]

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Absorption and Emission Bands

Band Shapes and Widths

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In Remote Sensing and Imaging

Multispectral Applications

Hyperspectral Applications

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Audio Signal Processing

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