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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
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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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LTI Systems, Continuous & Discrete Convolution Workbench

Interactive laboratory exploring continuous-time convolution integral y(t) = ∫x(τ)h(t-τ)dτ via the graphical flip-and-shift method with dynamic overlap area shading, discrete-time convolution sum y[n] = ∑x[k]h[n-k] with sliding stem plots, step response derivation s(t) = ∫h(τ)dτ, and LTI causality and BIBO stability criteria.

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Continuous & Discrete Fourier Analysis & Frequency Response Lab

Interactive laboratory exploring Continuous-Time Fourier Series (CTFS) harmonic synthesis with Gibbs phenomenon analysis, Continuous-Time Fourier Transform (CTFT) time-frequency duality, Discrete-Time Fourier Transform (DTFT) 2π-periodicity, and LTI frequency response H(jω) active filtering.

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Bilateral Laplace & Z-Transform Pole-Zero Stability Workbench

Interactive multi-domain laboratory exploring continuous s-plane and discrete z-plane pole-zero geometry, Region of Convergence (ROC) topology, BIBO stability theorems, and the conformal mapping z = e^(s Ts).

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