Pulssivaste

Pulssivaste, literally pulse response, is a concept used in signal processing and systems engineering to describe how a system reacts over time to a pulsed input. In many contexts it serves as a practical approximation of the impulse response of a linear time-invariant system, since a very short pulse can approximate a Dirac delta function when an ideal impulse is not feasible to generate. The pulssivaste thus contains the time-domain information needed to predict the system’s output for any input through convolution.

Mathematically, for a continuous-time system, the output y(t) is the convolution of the input x(t) with the impulse response h(t): y(t) = ∫ h(τ) x(t−τ) dτ. If the input is a delta function, x(t) = δ(t), then y(t) = h(t). In discrete time, y[n] = ∑ h[k] x[n−k]. The frequency response H(ω) is obtained by taking the Fourier transform of h(t). Important properties of pulssivaste in LTI systems include causality, stability, and time invariance; the shape of h(t) encodes how energy in the input is redistributed over time.

Measurement and estimation often use a short excitation pulse or an actual impulse to estimate h(t). In acoustics and room characterization, techniques such as exponential sine sweeps or MLS signals are used, followed by deconvolution to recover the impulse response. Practical considerations include noise, windowing, and deconvolution accuracy.

Applications of pulssivaste span audio equipment characterization (speakers, microphones, headphones), room acoustics, digital filter design, system identification, and communications channel analysis. Related concepts include the impulse response, step response, and transfer function.