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Figures 2-5 further illustrate construction of Bode plots. This example with both a pole and a zero shows how to use superposition. To begin, the components are presented separately. Figure 2 shows the Bode magnitude plot for a zero and a low-pass pole, and compares the two with the Bode straight line plots.
Statistical analyses of multivariate data often involve exploratory studies of the way in which the variables change in relation to one another and this may be followed up by explicit statistical models involving the covariance matrix of the variables. Thus the estimation of covariance matrices directly from observational data plays two roles:
# set terminal svg enhanced size 875 1250 fname "Times" fsize 25 set terminal postscript enhanced portrait dashed lw 1 "Helvetica" 14 set output "bode.ps" # ugly part of something G(w,n) = 0 * w * n + 100000 # 1 / (sqrt(1 + w**(2*n))) dB(x) = 0 + x + 100000 # 20 * log10(abs(x)) P(w) = w * 0 + 200 # -atan(w)*180/pi # Gridlines set grid # Set x axis to logarithmic scale set logscale x 10 set ...
In his example, there is a speed dating event set up in which there are two sets of what he terms "stooge dates": a set of males and a set of females. The experimenter selects 18 individuals, 9 males and 9 females to play stooge dates. Stooge dates are individuals who are chosen by the experimenter and they vary in attractiveness and personality.
Sometimes other ratios are more convenient than the 3 dB point. For instance, in the case of the Chebyshev filter it is usual to define the cutoff frequency as the point after the last peak in the frequency response at which the level has fallen to the design value of the passband ripple.
In enzyme kinetics, a secondary plot uses the intercept or slope from several Lineweaver–Burk plots to find additional kinetic constants. [1] [2]For example, when a set of v by [S] curves from an enzyme with a ping–pong mechanism (varying substrate A, fixed substrate B) are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced.
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let L be the loop transfer function and S be the sensitivity function .
The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. [ 1 ] [ 2 ] [ 3 ] It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response .