Discrete-time signals

Discrete-timesignals

A discrete-time signal is a sequence or a series of signal values defined in

discrete points of time, see Figure 1. These discrete points of time can be

denoted tk where k is an integer time index. The distance in time between

each point of time is the time-step, which can be denoted h. Thus,

h = tk − tk−1 (1)

The time series can be written in various ways:

{x(tk)} = {x(kh)} = {x(k)} = x(0), x(1), x(2), . . . (2)

To make the notation simple, we can write the signal as x(tk) or x(k).

Examples of discrete-time signals are logged measurements, the input signal to and the output signal from a signal filter, the control signal to a physical

process controlled by a computer, and the simulated response for a dynamic

system.

Piezoelectricity

Piezoelectricity is the charge which accumulates in certain solid materials (notably crystals, certain ceramics, and biological matter such as bone, DNA and various proteins) in response to applied mechanical strain. The word piezoelectricity means electricity resulting from pressure. It is derived from the Greek piezo or piezein, which means to squeeze or press, and electric or electron, which stands for amber, an ancient source of electric charge. Piezoelectricity is the direct result of the piezoelectric effect.

The piezoelectric effect is understood as the linear electromechanical interaction between the mechanical and the electrical state in crystalline materials with no inversion symmetry. The piezoelectric effect is a reversible process in that materials exhibiting the direct piezoelectric effect (the internal generation of electrical charge resulting from an applied mechanical force) also exhibit the reverse piezoelectric effect (the internal generation of a mechanical force resulting from an applied electrical field). For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their static structure is deformed by about 0.1% of the original dimension. Conversely, those same crystals will change about 0.1% of their static dimension when an external electric field is applied to the material.

Piezoelectricity is found in useful applications such as the production and detection of sound, generation of high voltages, electronic frequency generation, microbalances, and ultrafine focusing of optical assemblies. It is also the basis of a number of scientific instrumental techniques with atomic resolution, the scanning probe microscopies such as STM, AFM, MTA, SNOM, etc., and everyday uses such as acting as the ignition source for cigarette lighters and push-start propane barbecues.