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It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
One of the main reasons for using a frequency-domain representation of a problem is to simplify the mathematical analysis. For mathematical systems governed by linear differential equations, a very important class of systems with many real-world applications, converting the description of the system from the time domain to a frequency domain converts the differential equations to algebraic ...
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 ...
4.Plotting the Magnitude Spectrum. The magnitude of the frequency-domain representation X[k] is plotted to analyze the spectral content. The magnitude spectrum shows how the energy of the signal is distributed across different frequencies, which is useful for identifying prominent frequency components. It is calculated as:
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, " phase diagram ", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of ...
The Smith chart graphical equivalent of using the transmission-line equation is to normalise , to plot the resulting point on a Z Smith chart and to draw a circle through that point centred at the Smith chart centre. The path along the arc of the circle represents how the impedance changes whilst moving along the transmission line.
With this defined, one can plot a curve of constant H in the phase space of system. The phase space is a graph with θ {\displaystyle \theta } along the horizontal axis and θ ˙ {\displaystyle {\dot {\theta }}} on the vertical axis – see the thumbnail to the right.
Magnitude response of a low pass filter with 6 dB per octave or 20 dB per decade roll-off. Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the frequency spectra of the two signals (for example, using the fast Fourier transform for discrete signals), and comparing the spectra to isolate the ...