timesampling

Timesampling is the process of converting a continuous-time signal into a discrete-time sequence by recording its amplitude at regular time instants. Each sample represents the signal value at a sampling time t_n = nT, where T is the sampling period and f_s = 1/T is the sampling frequency.

According to the Nyquist-Shannon sampling theorem, a signal that is strictly bandlimited to B Hz can be perfectly reconstructed from its samples if f_s > 2B. In practice, anti-aliasing filters are used before sampling to enforce the bandlimit and reduce high-frequency components that would alias. Aliasing occurs when frequencies above half the sampling rate fold into lower frequencies, distorting the spectrum. Reconstruction from samples is possible if the sampling meets the condition, using an ideal reconstruction filter (sinc interpolation) or practical approximations such as zero-order hold, linear, or polyphase reconstructors.

Nonuniform sampling refers to sampling at irregular intervals, caused by jitter or asynchronous measurements; it requires more sophisticated algorithms and cannot, in general, be modeled as simple decimation by a fixed T. Timing inaccuracies, or jitter, can degrade reconstruction quality even when average sampling matches the Nyquist rate.

Important practical considerations include clock stability, timing jitter, aperture effects (the finite duration of a sampling window), and quantization error introduced during analog-to-digital conversion. Timesampling underpins digital audio, telecommunications, instrumentation, data acquisition, and many control systems, enabling storage, processing, and transmission of signals in a discrete form.