ECE 210 supplemental resource

Interactive Visuals

Short, visual demos for building intuition across time-domain, frequency-domain, and s-domain ideas in analog signal processing.

Time domain
signals, convolution, responses
Frequency domain
spectra, bandwidth, modulation
s-domain
Laplace, poles, circuits
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Important: These visualizations are experimental supplementary materials. They may contain mistakes or simplifications. Use them as intuition-building aids, not as an authoritative source for definitions, notation, or grading expectations.

Complex numbers and phasors

The Angle Challenge
Practice angle representations, reference angles, and conversions.
Complex Numbers and Phasors
Explore magnitude, phase, rectangular form, polar form, and Euler’s identity.

LTI systems, responses, and properties

ZIR, ZSR, and Superposition
Build intuition for zero-input response, zero-state response, and how they combine.
Impulse Response and Step Response
Compare step response, derivatives, and the true impulse response.
System Properties Explorer
Test causality, BIBO stability, linearity, and time invariance on example systems.
Recovering h(t) from g(t)
See why the impulse response is the derivative of the step response.
BIBO Stability and Causality from h(t)
Use the impulse response to judge stability and causality directly.

Convolution and impulses

Interactive Convolution
Visualize continuous-time convolution by flipping, shifting, multiplying, and integrating.
Continuous Convolution Visualization
A second convolution demo with a different presentation and perspective.
Dirac Impulse and Sifting Property
Develop intuition for impulses, weighted impulses, and the sifting property.
Impulses and Convolution Sandbox
Experiment with impulse-based constructions and their effect on convolution.

Fourier series and Fourier transform

Harmonics and Superposition
See how sinusoidal harmonics combine to form richer signals.
Fourier Series Visualization
Explore Fourier series coefficients and signal reconstruction.
Fourier Series Multi-Form Visualization
Compare multiple forms and views of Fourier series representations.
From Fourier Series to Fourier Transform
Build intuition for the limiting transition from periodic spectra to continuous spectra.
Fourier Quantities Explorer
Interact with energy, spectra, and bandwidth-related quantities in the Fourier domain.

Sampling, modulation, and aliasing

Sampling, Reconstruction, and Aliasing
See how sampling rate affects spectral replication, aliasing, and reconstruction.
Modulation, Frequency Shifting, and Low-Pass Filtering
Explore mixing, spectral shifting, and low-pass filtering in a modulation pipeline.
Continuous-Time Sampling and Reconstruction
A more detailed sampling demo showing replicas, aliasing, and recovery conditions.

Laplace transform and s-domain analysis

Laplace Transform and Region of Convergence
Connect time-domain decay or growth to convergence regions in the s-plane.
Poles, Modes, and Stability
Move poles in the s-plane and see the corresponding time-domain modes.
Inverse Laplace and Partial Fractions
Relate rational transforms, poles, residues, and time-domain components.
s-Domain Circuit Translation
Translate capacitors, inductors, and sources into algebraic s-domain circuit models.
Zero-State and Zero-Input Response with Laplace
Compare input-driven and initial-condition-driven parts of a circuit response.
LTIC ODEs and Laplace Transforms
Connect differential equations, transfer functions, modes, and total response.