Engineering Hub/Signal Processing & Communication/Signal Operations & System Properties Workbench

Signal Processing & CommunicationDiscipline: Signals and Systems (EEE2006)

Signal Operations & System Properties Workbench

Interactive laboratory exploring continuous and discrete signal operations (time shifting, time scaling, reversal, amplitude gain), orthogonal even and odd signal decomposition, energy vs. power signal classification with live integral solvers, and 6 core system axiom evaluations (linearity, time invariance, causality, BIBO stability, memory, and invertibility).

Instrument State:Live Analytical DSP Engine

Signal Operations & System Properties WorkbenchEEE2006 Unit 1

Transformation Engine (Shift, Scale, Reversal), Even/Odd Decomposition, Energy/Power Classifier & System Axiom Tests

Transformation Controlsy(t) = 1.5 · x(1.0(t - 1.0))

Base Signal x(t):

Time Shift (t₀):+1.0 s (Delay)

-3.0 (Left / Advance)0+3.0 (Right / Delay)

Time Scaling Factor (a):1.0×

-2.0 (Reverse+Comp)1.0+2.0 (Compress)

Amplitude Gain (A):1.5×

Order of Independent Variable Transformation:

Shift first, then scale: a(t - t₀)Scale first, then shift: (at - t₀)

Waveform Visualizer: x(t) vs y(t)

Original x(t) Transformed y(t)

Time Shift: Delays signal right by 1 s.Scaling: Normal scale.Reversal: Standard time direction.

Technical Instrument Specifications

Signal OperationsContinuous time shifting t - t0, scaling x(at), reversal x(-t), and order precedence

Even / Odd Slicesx(t) = xe(t) + xo(t) orthogonal decomposition with energy conservation Ex = Exe + Exo

Energy vs PowerTotal energy E = ∫|x(t)|²dt and average power P = lim (1/2T)∫|x(t)|²dt integral calculators

6 System AxiomsReal-time truth matrix for Linearity, Time Invariance, Causality, Stability, Memory, and Invertibility

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