Signalsin

Signalsin is a term used in signal processing to denote a sinusoidal electrical or digital signal. It is commonly used to model periodic inputs or test signals. In continuous time, a signalsin with amplitude A, frequency f, and phase φ is written as x(t) = A sin(2π f t + φ). Equivalently, x(t) = A sin(ω t + φ) with ω = 2π f. In discrete time, samples are x[n] = A sin(2π f n / fs + φ), where fs is the sampling frequency.

Characteristics: signalsin is periodic with period T = 1/f, assuming f > 0. It is bounded by ±A and is fully described by its amplitude, frequency, and phase. Its spectrum is a pair of delta lines at ±f in the continuous-time Fourier transform. When combined with other sinusoids, it forms complex signals or Fourier series.

Variants: a damped or windowed version may include an exponential factor, x(t) = A e^{-α t} sin(ω t + φ). In digital systems, a sine wave generator may include phase increments and numerical considerations to reduce quantization error.

Applications: used as a reference input for characterizing linear systems, testing filters and amplifiers, and as a fundamental component in modulation schemes and spectral analysis.

Implementation: in software and hardware, signalsin generators are implemented as oscillators or waveform blocks often labeled as sine wave sources, tone generators, or sinusoidal oscillators.

See also: sine wave, sinusoid, Fourier transform, oscillator, signal generator.

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