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The period (symbol T) is the interval of time between events, so the period is the reciprocal of the frequency: T = 1/f. [ 2 ] Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals ( sound ), radio waves , and light .
This relationship between event magnitude and frequency of occurrence is remarkably common, although the values of a and b may vary significantly from region to region or over time. GR law plotted for various b-values. The parameter b (commonly referred to as the "b-value") is commonly close to 1.0 in seismically active regions.
The cutoff frequency when expressed as an angular frequency (=) is simply the reciprocal of the time constant. Short conditional equations using the value for 10 6 / ( 2 π ) {\displaystyle 10^{6}/(2\pi )} :
Since ω = 2πf, =, and, since T = 1 / f where T is the time period, =. These equations demonstrate that the simple harmonic motion is isochronous (the period and frequency are independent of the amplitude and the initial phase of the motion).
A duty cycle or power cycle is the fraction of one period in which a signal or system is active. [1] [2] [3] Duty cycle is commonly expressed as a percentage or a ratio. A period is the time it takes for a signal to complete an on-and-off cycle. As a formula, a duty cycle (%) may be expressed as: = % [2]
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase ) of a complex-valued function s ( t ), is the real-valued function:
Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between signal cycles) with respect to a reference. [3]
In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at low ...