Signals & Systems

An analysis-and-education toolkit for the signals-and-systems core: linear convolution shown term by term, the DFT/FFT magnitude and phase spectrum with a correct Hz axis, the Fourier-series harmonics of the standard waveforms with a live partial-sum reconstruction (Gibbs and all), the sampling theorem with a concrete aliasing verdict, and the standard amplitude/energy metrics of a signal. Two tools analyze a given LTI system — its frequency response and its step/impulse response — by reusing the same tested transfer-function engine as the Control Systems toolkit. Every tool states its conventions explicitly (continuous vs discrete, DFT normalization, one- vs two-sided, rad/s vs Hz) because in this subject a silent convention mismatch changes the numbers. These are teaching and analysis tools, not a design of any physical system.

Convolution Calculator

Convolve two discrete sequences, y[n] = Σ x[k]·h[n−k], with the full flip-and-slide breakdown for the selected output sample and stem plots of both inputs and the result.

DFT / FFT Spectrum Analyzer

Compute the single-sided amplitude and phase spectrum of a sampled signal (generated from a waveform or entered directly) on a correct hertz axis, with the DFT normalization stated.

Fourier Series Calculator

Harmonic coefficients of the standard periodic waveforms with a live N-harmonic partial-sum reconstruction against the ideal — the Gibbs overshoot visible as you add terms.

Sampling & Aliasing Calculator

From a signal frequency and a sample rate: the Nyquist rate, whether the tone is aliased, and the exact folded (apparent) frequency the samples appear to contain.

Signal Metrics Calculator

RMS, mean, average power, energy, peak, peak-to-peak, and crest factor of a signal — generated from a standard waveform or entered as samples.

Frequency Response of an LTI System

Analyze a GIVEN continuous-time LTI system H(s): its magnitude (dB) and phase response H(jω) on a log-frequency axis, evaluated exactly, with the value at any chosen frequency.

Step / Impulse Response of an LTI System

Simulate the step or impulse response of a GIVEN continuous-time LTI system H(s), with the standard time-domain metrics (overshoot, rise, peak, settling) for the step.