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SIG:010117The scaled reversed triangle x(2-3t) lives on [1/3,1], has energy 2/9, and is not an LTI test

Sas Triangle Scale Reverse SupportSas Time Scale Energy Jacobian

Signal spaces and LTI systemsSignals and Systems · Mixed review

SIG:010118The everlasting 3 cos(2 pi t) has power 9/2; its [-1,1] window has energy 9; the two-tone sequence has period 12 and power 1

Sas Energy Power Signal ClassSas Discrete Period Average Power

Signal spaces and LTI systemsSignals and Systems · Mixed review

SIG:010219Linear convolution of [1,-2,1] with [1,1,1] is [1,-1,0,-1,1] and deconvolution recovers the input

Sas Discrete Linear Convolution SumSas Fir Generating Function Deconvolution

Continuous and discrete convolutionSignals and Systems · Mixed review

SIG:010220Mathematical problem title

Sas Causal Exponential Overlap IntegralSas Repeated Pole Convolution Limit

Continuous and discrete convolutionSignals and Systems · Mixed review

SIG:010221Mathematical problem title

Sas Impulse Train Distributional SiftingSas Step Breakpoint Piecewise Audit

Continuous and discrete convolutionSignals and Systems · Mixed review

SIG:010322Time weighting differentiates the spectrum and changes its energy.

Time Weight FT DerivativeParseval Energy Time Weight

Fourier series and transformsSignals and Systems · Mixed review

SIG:010323Modulation shifts two spectra, but overlapping lobes keep a cross term.

Cosine Modulation ShiftOverlapping Lobe Cross Energy

Fourier series and transformsSignals and Systems · Mixed review

SIG:010424The unilateral z-transform must carry the sample before zero.

Unilateral Z Delay PropertyInitial Rest Recurrence Solve

Laplace and z transformsSignals and Systems · Mixed review

SIG:010425A repeated pole creates the polynomial factor, not a second exponential.

Repeated Pole N Plus OneGeometric Polynomial Energy Sum

Laplace and z transformsSignals and Systems · Mixed review

SIG:010526Sampling can be alias-free while the hold still droops and delays the waveform.

Zoh Frequency ResponseSinc Droop Linear Phase

Sampling, aliasing, and reconstructionSignals and Systems · Mixed review

SIG:010527Alternating clock jitter creates a deterministic image spur, not random noise

Deterministic Alternating Jitter ExpansionDiscrete Image Spur Amplitude

Sampling, aliasing, and reconstructionSignals and Systems · Mixed review

SIG:010628Stable eigenvalues can amplify the state before every mode decays

Matrix Exponential Upper TriangularNonnormal Transient Peak

State-space systems, causality, and stabilitySignals and Systems · Mixed review

SIG:010629Observability is quantitative: the Gramian prices every initial direction

Observability Gramian IntegralOutput Energy Quadratic Form

State-space systems, causality, and stabilitySignals and Systems · Mixed review

SIG:010630One input-output energy ratio is not the induced L2 gain

Induced L2 H Infinity NormOne Input Energy Ratio Gap

State-space systems, causality, and stabilitySignals and Systems · Mixed review

SIG:010631The finite-horizon Gramian finds the least-energy input pair exactly

Finite Horizon Reachability GramianMinimum Energy Steering Input

State-space systems, causality, and stabilitySignals and Systems · Mixed review