Signals and Systems¶
Oppenheim, A. V., Willsky, A. S., S. Hamid Nawab, S., & Systems, 2. e. (1996). Signals and Systems. Prentice Hall.
Retired. This is not a bibliographic entry. Our extractor captured an inline prose definition from an article and stored it as a work. The concept is real; this registry record is a parsing defect. This entry is kept so the citations that pointed at it still resolve, and so the correction is visible rather than silent.
Cited by¶
8 citations across 8 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Convolution
- In continuous form \((f * g)(t) = \int f(\tau)\, g(t-\tau)\, d\tau\), and in discrete form the corresponding sum; in both, the second function is flipped and slid across the first.
This sourceDefines the continuous and discrete convolution, the flip-and-slide operation, LTI impulse response, translation invariance, the convolution theorem, and the operation's commutativity/associativity/identity algebra.
- In continuous form \((f * g)(t) = \int f(\tau)\, g(t-\tau)\, d\tau\), and in discrete form the corresponding sum; in both, the second function is flipped and slid across the first.
- Harmonic Distortion
- Harmonic distortion is the structural pattern in which a signal passed through a nonlinear transfer function emerges carrying new frequency components — harmonics at integer multiples of the input frequencies, and intermodulation products at their sums and differences — that were not present in the input at all.
This sourceStandard text: linear systems cannot create new frequencies, while a nonlinear (memoryless) map raises a signal to powers, generating harmonics at integer multiples and intermodulation products at sums and differences.
- Harmonic distortion is the structural pattern in which a signal passed through a nonlinear transfer function emerges carrying new frequency components — harmonics at integer multiples of the input frequencies, and intermodulation products at their sums and differences — that were not present in the input at all.
- Reference Cadence Exceeds Tracking Bandwidth
- The error-spectrum diagnostic is exact and measurable: take the Fourier transform of the tracking error and observe that it is concentrated above 10 Hz — that spectral signature is the proof that the failure is bandwidth mismatch, not a sluggish or mis-tuned controller, because below 10 Hz the same loop tracks faithfully.
This sourceStandard treatment of frequency-domain analysis, spectra of error signals, and aliasing under undersampling.
- The error-spectrum diagnostic is exact and measurable: take the Fourier transform of the tracking error and observe that it is concentrated above 10 Hz — that spectral signature is the proof that the failure is bandwidth mismatch, not a sluggish or mis-tuned controller, because below 10 Hz the same loop tracks faithfully.
- Vector Space
- Signal processing: signals as elements of \(L^2\); Fourier analysis as basis decomposition in a function space.
This sourceSignals as elements of a function space and Fourier analysis as basis decomposition.
- Signal processing: signals as elements of \(L^2\); Fourier analysis as basis decomposition in a function space.
Domain-specific¶
- Harmonic Spectrum
- Square wave. An ideal symmetric square wave contains odd harmonics \(f_0,3f_0,5f_0,\ldots\) with amplitudes decreasing in inverse proportion to harmonic number, the \(n\)th harmonic scaling as \(1/n\)
This sourceSupplies the Fourier-series derivation showing a symmetric square wave's odd harmonics scale in amplitude as 1/n.
SupportedVerified against the source
- Square wave. An ideal symmetric square wave contains odd harmonics \(f_0,3f_0,5f_0,\ldots\) with amplitudes decreasing in inverse proportion to harmonic number, the \(n\)th harmonic scaling as \(1/n\)
- Hermitian function
Mechanisms¶
- Decay-Weighted Score Update
- Recency-weighting is the standard, well-understood way to do this.
This sourceDevelops the standard recursive-filter form that gives newer observations greater weight while exponentially decaying prior contributions.
- Recency-weighting is the standard, well-understood way to do this.
- Exponential Leaky Integrator
- Because old events fade rather than vanish, a burst leaves a long exponential tail: the estimate stays elevated well after the burst is over, and a step change is approached only asymptotically, never reached, so the integrator systematically lags a rising signal.
This sourceDerives the exponential memory and asymptotic step response of a first-order system, including its persistent tail and lag.
- Because old events fade rather than vanish, a burst leaves a long exponential tail: the estimate stays elevated well after the burst is over, and a step change is approached only asymptotically, never reached, so the integrator systematically lags a rising signal.
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Read against the text for 1 of 8 citations: 1 supported. Each verdict is shown under its citation below, with what in the work backs the sentence.
Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 4 other ways.
- https://search.worldcat.org/title/Signals-and-systems/oclc/1006312847 ×2
- https://www.pearson.com/en-us/subject-catalog/p/signals-and-systems/P200000003155 ×2
- https://archive.org/details/oppenheim-willsky-nawab-signals-systems-2nd-edition ×1
- https://www.pearson.com/en-us/subject-catalog/p/signals-and-systems/P200000003155/9780138147570 ×1
Registry ID ref:7ea1ad9b5b36 · see in the full table