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The period T is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation [4] =. The term temporal frequency is used to emphasise that the frequency is characterised by the number of occurrences of a repeating event per unit time.
In a rotating or orbiting object, there is a relation between distance from the axis, , tangential speed, , and the angular frequency of the rotation. During one period, T {\displaystyle T} , a body in circular motion travels a distance v T {\displaystyle vT} .
For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
When two signals with these waveforms, same period, and opposite phases are added together, the sum + is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes. The phase shift of the co-sine function relative to the sine function is +90°.
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
Consider a real waveform consisting of superimposed frequencies, expressed in a set as ratios to a fundamental frequency, f: F = 1 ⁄ f [f 1 f 2 f 3... f N] where all non-zero elements ≥1 and at least one of the elements of the set is 1. To find the period, T, first find the least common denominator of all the elements in the set.
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:
For example, a signal (10101010) has 50% duty cycle, because the pulse remains high for 1/2 of the period or low for 1/2 of the period. Similarly, for pulse (10001000) the duty cycle will be 25% because the pulse remains high only for 1/4 of the period and remains low for 3/4 of the period. Electrical motors typically use less than a 100% duty ...