A. V. Oppenheim, A. S. Willsky & S. Hamid Nawab, Signals and Systems, 2nd ed., Prentice Hall, 1997.
Continuous-time signals, independent variables, elementary signal descriptions, transformations and systems vocabulary.
SG-01
Course overview
Signals in time: DC, variable & sinusoidal quantities
Before phasors, frequency response or oscilloscopes, a signal must first be readable in time. This course builds that language from the ground up: physical quantity versus mathematical representation, constant and time-varying behavior, amplitude and offset, period and frequency, phase, sinusoidal notation and disciplined reading of time plots.
5 chapters5 available · 0 plannedfoundational
Prerequisites
- EF-01 — reference directions & notation
- MS-01 — DC electrical measurement
- Elementary algebra
By the end of the course
- Distinguish a physical quantity, its time function and a measurement record.
- Read a waveform correctly using axes, units, instantaneous values and intervals.
- Distinguish constant, time-varying, periodic, sinusoidal and sign-changing behavior.
- Define amplitude, offset, period, frequency and phase without ambiguity.
- Write and interpret a real sinusoidal time function before introducing phasors.
- Turn a time plot into a quantitative signal description ready for AC-01 and MS-02.
Syllabus
Five readings to learn how to read and describe a signal before phasors.
Before phasors, frequency response or oscilloscopes, a signal must first be readable in time. This course builds that language from the ground up: physical quantity versus mathematical representation, constant and time-varying behavior, amplitude and offset, period and frequency, phase, sinusoidal notation and disciplined reading of time plots.
- 01→
From a physical quantity to x(t): constant & time-varying signals
Build the time-domain language before using sinusoidal formulas: independent variable, value at an instant, waveform, units, AoN notation, constant versus time-varying behavior, piecewise models, continuous-time functions versus measured samples, and the limits of idealized jumps.
120–150 min · Foundational · available - 02→
Peak values, amplitude, offset & period
Turn a waveform into quantitative descriptors without abusing the word amplitude. Define maxima/minima and peak-to-peak value, distinguish vertical offset from time average, derive the mean of a periodic signal, define periodicity and fundamental period rigorously, handle constant-signal edge cases, and separate waveform shape from vertical/time shifts.
125–155 min · Foundational · available - 03→
Frequency, angular frequency & phase from time shifts
Convert repetition time into cycles per second, introduce angular frequency without losing units, then define phase through relative position within a cycle. Derive the sign of phase for a delayed cosine, distinguish phase lead/lag from time delay, handle modulo-2π equivalence, and explain why a single fixed phase difference requires equal frequency.
130–165 min · Foundational · available - 04→
Sinusoidal waveforms: from equation to engineering quantities
Assemble offset, peak amplitude, angular frequency and phase into one real sinusoidal model. Derive extrema, peak-to-peak value, average and root-mean-square value, relate sine and cosine conventions, resolve negative-amplitude ambiguity, read initial value and time landmarks, and connect waveform slope to bandwidth-aware measurement intuition.
135–170 min · Foundational · available - 05→
From time plots to defensible signal descriptions
Synthesize SG-01 into a repeatable engineering workflow: identify the physical quantity and reference, read units and observation window, classify behavior without overclaiming periodicity, extract vertical and temporal descriptors, separate average and zero-mean variation, fit a sinusoidal model only when justified, validate phase and RMS independently, and document what came from the mathematical model versus a finite measurement record.
140–180 min · Foundational · available
Reference backbone
References used
AoN separates physical quantities, mathematical signal models and instrument observations. Signal notation follows the established AoN electrical convention; units remain SI quantities; later phasor and transform notation is deliberately not introduced until the time-domain concepts are stable.
B. P. Lathi & R. A. Green, Linear Systems and Signals, 3rd ed., Oxford University Press, 2018.
Time-domain signal descriptions, periodicity, sinusoidal parameters and worked engineering interpretation.
S. Haykin & B. Van Veen, Signals and Systems, 2nd ed., Wiley, 2003.
Signal classification, continuous-time descriptions and signal/system intuition.
BIPM, The International System of Units (SI Brochure), 9th ed.
SI quantity/unit discipline, especially time in seconds and electrical quantities in their proper units.
AoN EF-01 — Reference directions and electrical notation.
Normative AoN notation: constant/DC electrical quantities uppercase; instantaneous time-domain quantities lowercase functions such as v(t) and i(t).
AoN MS-01 — DC electrical measurement.
Bridge from an ideal mathematical time function to finite instrument observations, loading and reproducible measurement evidence.