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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 .
It is sometimes taken to be the point in the filter response where a transition band and passband meet, for example, as defined by a half-power point (a frequency for which the output of the circuit is approximately −3.01 dB of the nominal passband value). Alternatively, a stopband corner frequency may be specified as a point where a ...
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 ...
The gain and the delay for this filter are plotted in the graph on the left. There are no ripples in the gain curve in either the passband or the stopband. The log of the absolute value of the transfer function () is plotted in complex frequency space in the second graph on the right. The function is defined by the three poles in the left half ...
Bode magnitude plot for the voltages across the elements of an RLC series circuit. Natural frequency ω 0 = 1 rad/s, damping ratio ζ = 0.4. Sinusoidal steady state is represented by letting s = jω, where j is the imaginary unit. Taking the magnitude of the above equation with this substitution:
For transfer functions (e.g., Bode plot, chirp) the complete frequency response may be graphed in two parts: power versus frequency and phase versus frequency—the phase spectral density, phase spectrum, or spectral phase. Less commonly, the two parts may be the real and imaginary parts of the transfer function.
The plots at the bottom show the signal intensity in the indicated row of the image (red: original signal, blue: with noise). Signal-to-noise ratio ( SNR or S/N ) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise .
The code is kind of kludgy, but makes a good output. Generated in gnuplot with the script below (save as butterworth_bode_plot.plt and then open in gnuplot). Then it was postprocessed with Inkscape. See Wikipedia graph-making tips. Many orders on one plot: Image:Butterworth orders.png