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Limiting a signal to contain only low-frequency components
Bandlimiting is the process of reducing a signal’s energy outside a specific frequency range, keeping only the desired part of the signal’s spectrum. This
Bandlimiting
Form of distortion affecting communication reliability
cable, the allocation will be decided by the owner of the cable. The bandlimiting can also be due to the physical properties of the medium - for instance
Intersymbol_interference
Non-sinusoidal waveform
available below. Both bandlimited (non-aliased) and aliased tones are presented. Sawtooth aliasing demo Sawtooth waves played bandlimited and aliased at 440 Hz
Sawtooth_wave
Compact encoding of digital data
uncompressed format and several lossy formats. The lossy spectrograms show bandlimiting of higher frequencies, a common technique associated with lossy audio
Data_compression
Signal processing effect
(constant). Sawtooth aliasing demo 440 Hz bandlimited, 440 Hz aliased, 880 Hz bandlimited, 880 Hz aliased, 1760 Hz bandlimited, 1760 Hz aliased Problems playing
Aliasing
Sufficiency theorem for reconstructing signals from samples
band-limiting filter, via its integral, the step-response sine integral; this bandlimiting and reconstruction filter that is so central to the sampling theorem
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Mathematical function
orthogonal basis for bandlimited or spacelimited spaces. That is, they are concentrated in space or time while spectrally bandlimited, or concentrated in
Slepian_function
When a signal or function exceeds its target
the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and
Overshoot_(signal)
Information-theoretical limit on transmission rate in a communication channel
Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably
Channel_capacity
Special mathematical function defined as sin(x)/x
no scaling. It is used in the concept of reconstructing a continuous bandlimited signal from uniformly spaced samples of that signal. The sinc filter
Sinc_function
Foundational principle in quantum physics
function and its Fourier transform cannot both have bounded domain)—see bandlimited versus timelimited. More accurately, the time-bandwidth or duration-bandwidth
Uncertainty_principle
Signal (re-)construction algorithm
formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
Representation of a signal as a rectangular wave with varying duty cycle
The PWM sampling theorem shows that PWM conversion can be perfect: Any bandlimited baseband signal whose amplitude is within ±0.637 (2/π) can be represented
Pulse-width_modulation
Function in discrete mathematics
frequencies have the smallest possible magnitudes: the interpolation is bandlimited. Second, if the x n {\displaystyle x_{n}} are real numbers, then p (
Discrete_Fourier_transform
Küpfmüller in the year 1924 states that the relation of the rise time of a bandlimited signal to its bandwidth is a constant. Δ f Δ t ≥ k {\displaystyle \Delta
Küpfmüller's uncertainty principle
Küpfmüller's_uncertainty_principle
Non-sinusoidal waveform
Wave Zigzag Kraft, Sebastian; Zölzer, Udo (5 September 2017). "LP-BLIT: Bandlimited Impulse Train Synthesis of Lowpass-filtered Waveforms". Proceedings of
Triangle_wave
Mathematical transformation reducing the damage caused by aliasing
one desired to sample an FM radio broadcast centered at 87.9 MHz and bandlimited to a 200 kHz band, then an appropriate anti-alias filter would be centered
Anti-aliasing_filter
Minimum sampling rate to avoid aliasing
functions that fit the same set of samples. But only one of them is bandlimited to 1 2 f s {\displaystyle {\tfrac {1}{2}}f_{s}} cycles/second (hertz)
Nyquist_rate
Israeli academic and engineer
and reception. Eldar is the author of the book Sampling Theory: Beyond Bandlimited Systems (2015) and co-author of Compressed Sensing (2012) and Convex
Yonina_Eldar
Changing the resolution of a digital image
in theory, provides the best possible reconstruction for a perfectly bandlimited signal. In practice, the assumptions behind sinc resampling are not completely
Image_scaling
Integral transform and linear operator
Figure 1: Filter whose frequency response is bandlimited to about 95% of the Nyquist frequency
Hilbert_transform
Form of error in digital signals; spurious signals near sharp transitions
design. The main cause of ringing artifacts is due to a signal being bandlimited (specifically, not having high frequencies) or passed through a low-pass
Ringing_artifacts
System for digitally encoding audio signals
used in linear PCM formats, where the ADC or DAC output is subject to bandlimiting and dithering. Most modern ADC and DAC converters use oversampling and
Direct_Stream_Digital
Model of signal reconstruction in digital-to-analog (DAC) converters
if ideally low-pass filtered, would result in the unique underlying bandlimited signal before sampling), but instead output a sequence of rectangular
Zero-order_hold
Electrical noise due to thermal vibration within a conductor
resistance R {\displaystyle R} at kelvin temperature T {\displaystyle T} and bandlimited to a frequency band of bandwidth Δ f {\displaystyle \Delta f} (Figure
Johnson–Nyquist_noise
Method for modulation of data
attribute is desirable for signals that are to be transmitted over a bandlimited channel, as discontinuities in a signal introduce wideband frequency
Continuous_phase_modulation
Type of electronic filter circuit
applications as lumped element filters, such as selectivity of radio channel, bandlimiting of noise and multiplexing of many signals into one channel. Distributed-element
Distributed-element_filter
In functional analysis, a Hilbert space
functions, as we now illustrate by example. Consider the Hilbert space of bandlimited continuous functions H {\displaystyle H} . Fix some cutoff frequency
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
System that converts an analog signal into a digital signal
neglected, resulting in an essentially perfect digital representation of the bandlimited analog input signal. The resolution of the converter indicates the number
Analog-to-digital_converter
Theorem in mathematics
distribution, such as the Dirac delta, is "rapidly decreasing". Equivalently, bandlimited functions, such as the function that is constantly 1 {\displaystyle 1}
Convolution_theorem
Basic noise model used in information theory
linear terms. In modern communication systems, bandlimited AWGN cannot be ignored. When modeling bandlimited AWGN in the phasor domain, statistical analysis
Additive_white_Gaussian_noise
Method for converting signals between digital and analog
may be a valid approximation provided that the input signal is already bandlimited and can be assumed to be not changing on time scales higher than the
Delta-sigma_modulation
Topics referred to by the same term
1957 drama film "Time Limit" (song), a 2000 R&B single by Hikaru Utada Bandlimiting This disambiguation page lists articles associated with the title Time
Time_limit_(disambiguation)
Process in electronics and telecommunications
interference as a result of Fourier correspondences (see Fourier transform). A bandlimited signal corresponds to an infinite time signal that causes neighboring
Pulse_shaping
Periodic rectangular waveform
phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is bandlimited, too. The pulse waveforms are non-sinusoidal that
Pulse_wave
Relative importance of certain frequencies in a composite signal
distribution F ( f ) {\displaystyle F(f)} , which specifies the average bandlimited power contained in frequencies from DC to f using: F ( f ) = 2 ∫ 0 f
Spectral_density
the two narrowband colour difference signals containing RN and BN, a bandlimited version of the luminance signal (y') is required, namely: y ′ = 0.3 R
EMI_2001
Analog of the continuous Laplace operator
grid K {\displaystyle K} . On a uniform grid, such as images, and for bandlimited functions, interpolation functions are shift invariant amounting to μ
Discrete_Laplace_operator
Technology that records, stores, and reproduces sound
resolution for each stereo channel. Analog signals that have not already been bandlimited must be passed through an anti-aliasing filter before conversion, to
Digital_audio
Filter used to construct a smooth analog signal from a digital input
filter, called the anti-aliasing filter: the sampled input signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being recorded
Reconstruction_filter
Improved version of VHS
chrominance (chroma) signal. In VHS, the chroma carrier is both severely bandlimited and noisy, a limitation that S-VHS does not address. Lack of color resolution
S-VHS
Common sampling frequency in digital audio
than 40 kHz. But to avoid aliasing when sampling, signals must first be bandlimited to within half the sampling frequency, which can be achieved with low-pass
44,100_Hz
Permutation that reverses binary numbers
Gordon, Dan (June 2017), "A derandomization approach to recovering bandlimited signals across a wide range of random sampling rates", Numerical Algorithms
Bit-reversal_permutation
Sound synthesis technique
output y ( t ) {\displaystyle y(t)\,} is expected to be sufficiently bandlimited; below half the sampling rate or f s / 2 {\displaystyle f_{\mathrm {s}
Additive_synthesis
Term for two forms of anti-aliasing
window function of the exposure (its shape over time) determines how well bandlimited the image signal is before sampling. Different window functions can be
Temporal_anti-aliasing
Synthesizer feature
Aug, 019132 synth-diy:2009, August, 019136 http://www.music.mcgill.ca:bandlimited https://www.cs.cmu.edu:icmc01-hardsync.pdf http://www.gersic.com:Physical
Oscillator_sync
Study of classical optics using Fourier transforms
holds for paraxial plane waves, so this FT "computer" is inherently bandlimited. On the other hand, since the wavelength of visible light is so minute
Fourier_optics
Integral transform
2383–2394, (2008). Ran Tao, Bing-Zhao Li, Yue Wang, "On sampling of bandlimited signals associated with the linear canonical transform", IEEE Transactions
Linear canonical transformation
Linear_canonical_transformation
American mathematician
for his contributions to information theory, including the theory of bandlimited functions and on moment problems. Landau was born to a Jewish family
Henry_Landau
number of samples required to represent the signal completely. For a bandlimited waveform, there are infinitely many ways the signal can be sampled without
Hexagonal_sampling
Topic in mathematics
An important class of such continuous-time stationary process is the bandlimited stationary ergodic process with the sample space being a subset of the
Asymptotic equipartition property
Asymptotic_equipartition_property
Digital signal resampling method
2024-01-31. "Digital Audio Resampling Home Page". (discusses a technique for bandlimited interpolation) "Matlab example of using polyphase filters for interpolation"
Upsampling
Algorithm to approximate functions
Temes, G.C.; Barcilon, V.; Marshall, F.C. (1973). "The optimization of bandlimited systems". Proceedings of the IEEE. 61 (2): 196–234. Bibcode:1973IEEEP
Remez_algorithm
Numerical integration method
Equivalently, the a 2 k {\displaystyle a_{2k}} are the amplitudes of the unique bandlimited trigonometric interpolation polynomial passing through the N+1 points
Clenshaw–Curtis_quadrature
Function that "converges" to periodicity
varying functions of time. Stated differently these functions of time are bandlimited to much less than the fundamental frequency for x ( t ) {\displaystyle
Almost_periodic_function
Algorithm
superiority of this selection was illustrated with the reconstruction of a bandlimited function from its nonuniformly spaced sampling values. However, it has
Kaczmarz_method
fact that the aperture is of limited size, resulting in the PSF being bandlimited (i.e., its Fourier transform has zeros). Instead, an iterative algorithm
Light_field_microscopy
; Zhang, N.-T. (2010). "Multichannel sampling and reconstruction of bandlimited signals in fractional Fourier domain". IEEE Signal Processing Letters
Fractional_wavelet_transform
Signal-processing paradigm that trades precision for volume of measurements
and one-bit Hankel matrix completion. Unlimited/one-bit sampling for bandlimited and finite-rate-of-innovation signals, and HDR imaging with sweeping
Sample_abundance
results of Iwahori-Sugiura, and Tatsuuma. Algorithms exist for recovering bandlimited functions from their triple correlation on Euclidean space, as well as
Triple_correlation
Audio effect
AUDIO APPLICATIONS". ccrma.stanford.edu. Retrieved 2023-07-06. "Ideal Bandlimited (Sinc) Interpolation". ccrma.stanford.edu. Retrieved 2023-07-06. Välimäki
Digital_delay_line
techniques, albeit in practice often a very good one. The concept of a bandlimited function in one dimension can be generalized to the notion of a wavenumber-limited
Multidimensional_sampling
Geophysical process
volumes from full or post-stack seismic data: full-bandwidth impedance, bandlimited Impedance, reflectivity model, and low-frequency component. Each of these
Seismic_inversion
Greek-American engineer and applied mathematician (1921–2002)
1080/713818946. Papoulis, A. (1975). "A new algorithm in spectral analysis and bandlimited extrapolation". IEEE Transactions on Circuits and Systems. 22 (9): 735–742
Athanasios_Papoulis
Theorem in sampling theory
sampling theory that shows that the sampling density of a two-dimensional bandlimited function can be reduced to the support of the Fourier transform of the
Papoulis-Marks-Cheung Approach
Papoulis-Marks-Cheung_Approach
aliased Doppler spectra of the N representations. This means that any bandlimited signal U ( f {\displaystyle U(f} is uniquely determined in terms of the
High Resolution Wide Swath SAR imaging
High_Resolution_Wide_Swath_SAR_imaging
for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems,
Shearlet
New Zealand physicist (1938–2018)
2022. Bold, Gary E.J.; Johns, Murray D. (1987). "Signals for optimum bandlimited system interrogation with application to underwater acoustics". The Journal
Gary_Bold
American engineer and intelligent design advocate (born 1950)
December 1992. R.J. Marks II, "Restoring lost samples from an oversampled bandlimited signal", IEEE Transactions on Acoustics, Speech, and Signal Processing
Robert_J._Marks_II
Electrical engineering problem
401-404, Apr.1979 A. Papoulis, “A new algorithm in spectral analysis and bandlimited extrapolation,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 735-742
Multidimensional signal restoration
Multidimensional_signal_restoration
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