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The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
Conversely, a phase reversal or phase inversion implies a 180-degree phase shift. [ 2 ] When the phase difference φ ( t ) {\displaystyle \varphi (t)} is a quarter of turn (a right angle, +90° = π/2 or −90° = 270° = −π/2 = 3π/2 ), sinusoidal signals are sometimes said to be in quadrature , e.g., in-phase and quadrature components of a ...
In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency.The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay.
In the case of reactive termination the phase shift will be between 0 and +180° for inductors and between 0 and −180° for capacitors. The phase shift will be exactly ±90° when |X| = Z 0. For the general case when the line is terminated with some arbitrary impedance, Z, the reflected wave is generally less than the incident wave.
The phase shifters delay the radio waves progressively going up the line so each antenna emits its wavefront later than the one below it. This causes the resulting plane wave to be directed at an angle θ to the antenna's axis. By changing the phase shifts, the computer can instantly change the angle θ of the beam. Most phased arrays have two ...
DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state , i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary ...
An example application of the Fourier transform is determining the constituent pitches in a musical waveform.This image is the result of applying a constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord.
The peak at time = 5 is a measure of the time shift between the recorded waveforms, which is also the value needed for equation 3. Figure 4b shows the same type of simulation for a wide-band waveform from the emitter. The time shift is 5 time units because the geometry and wave speed is the same as the Figure 4a example.