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# Bode plot

A Bode magnitude plot is a graph of log(magnitude) against log(frequency) often used in signal processing to show the transfer function of a system. It makes multiplication of magnitudes a simple matter of adding distances on the graph, since log(a×b) = log(a)+log(b). The Bode plot describes the output response of a frequency-dependent system for a normalised input.

A Bode phase plot is a graph of phase against log(frequency), usually used in conjunction with the magnitude plot, to evaluate how much a frequency will be phase-shifted. For example a signal described by: A×sint) may be attenuated but also phase-shifted. If the system attenuates it by a factor x and phase shifts it by -Φ the signal out of the system will be A/x×sint-Φ). The phase shift Φ is generally a function of frequency.

The magnitude and phase Bode plots can seldom be changed independently of each other—if you change the amplitude response of the system you will most likely change the phase characteristics as well and vice versa.

A typical application of a Bode plot is to show the frequency response of a filter. It is especially useful in this case because the complex curves that appear in a linear magnitude-frequency plot can often be approximated by straight lines in a Bode plot.

Another often used plot is the Nyquist plot