Amplitude is a measure of the strength or magnitude of a signal. In the context of a sinusoidal signal, it is the peak value reached by the waveform — the distance from zero to the maximum (or minimum) value. A larger amplitude means a louder sound, a brighter light, or a stronger electrical signal.
A pure sinusoid is described by three parameters:
$x(t) = A \cdot \sin(2\pi f t + \phi)$
where $A$ is the amplitude — the peak deviation from zero. In this equation, $A$ controls the vertical size of the wave, while $f$ controls its speed (frequency) and $\phi$ controls its horizontal shift (phase).
The plot above shows three sine waves with the same frequency (5 Hz) and phase (0°), but different amplitudes. The blue wave has amplitude 1.0, the orange wave has amplitude 0.5, and the green wave has amplitude 0.25. As the amplitude decreases, the signal becomes weaker — its peaks and troughs are closer to zero.
In signal processing, amplitude appears in several important contexts:
- Time domain: The amplitude of a signal is its instantaneous value at any point in time. The peak amplitude is the maximum absolute value reached.
- Frequency domain: The magnitude spectrum $|X[k]|$ shows the amplitude of each frequency component present in the signal.
- Units: Amplitude can be measured in volts (electrical signals), Pascals (sound pressure), or any other physical unit that represents signal strength.
- Decibels (dB): Amplitude is often expressed in decibels — a logarithmic scale that compresses a wide dynamic range into a manageable scale.
Amplitude and energy: The energy of a signal is proportional to the square of its amplitude. Doubling the amplitude quadruples the energy. This is why amplitude is often described in terms of root‑mean‑square (RMS) values for power calculations.
Amplitude vs magnitude: In DSP literature, the terms "amplitude" and "magnitude" are sometimes used interchangeably, but they have subtle differences. Amplitude typically refers to the peak value of a time‑domain signal. Magnitude usually refers to the absolute value of a complex number in the frequency domain (or any vector). In many contexts, however, the distinction is not strict.