Waveforms

A waveform is a graphical representation of how a quantity varies with time, typically showing amplitude on the vertical axis and time on the horizontal axis. In electronics and signal processing, a waveform often refers to how a voltage, current, or other physical quantity changes over time.

Waveforms are classified as periodic or aperiodic. Periodic waveforms repeat at regular intervals and are described by a fundamental frequency. Common periodic waveforms include sine, square, triangle, and sawtooth waves. Aperiodic waveforms do not repeat regularly and include signals such as speech and most environmental noises. Each waveform is characterized by parameters such as amplitude, frequency, phase, and, for non-sinusoidal shapes, features like duty cycle, rise and fall times, and harmonic content.

Frequency-domain analysis describes waveforms in terms of their spectral components. The Fourier series expresses a periodic waveform as a sum of sine and cosine terms at harmonic intervals of the fundamental frequency, with coefficients that determine the amplitude of each harmonic. A sine wave is a single-frequency signal, while square, triangle, and sawtooth waves contain multiple harmonics, with amplitudes following characteristic patterns: square waves contain odd harmonics with amplitudes proportional to 1/n, triangle waves decay as 1/n^2, and sawtooth waves include all harmonics with amplitudes proportional to 1/n.

Generation and shaping of waveforms are central to electronic design. Oscillators and function generators produce basic waveforms, which can be shaped by modulation, pulse-width modulation, and filters. Digital synthesis and DACs implement complex waveforms in software and hardware. Measurement uses oscilloscopes for time-domain views and spectrum analyzers or FFTs for frequency-domain content, with sampling considerations to avoid aliasing.

Applications span communications, audio production, instrumentation, and testing, where waveform quality and spectral content affect performance and signal integrity.