#### Weighted digital filter design

Many methods for digital filter design support spectral weighting functions that can be used to focus in on the least-damped modes in the frequency response. One is the

*weighted equation-error*method which is available in the matlab

`invfreqz()`function (§8.6.4). Figure 8.13 illustrates use of it. For simplicity, only one frequency-response peak plus noise is shown in this synthetic example. First, the peak center-frequency is measured using a quadratically interpolating peak finder operating on the dB spectral magnitude. This is used to set the spectral weighting function. Next,

`invfreqz()`is called to design a two-pole filter having a frequency response that approximates the measured data as closely as possible. The weighting function is also shown in Fig.8.13, renormalized to overlay on the scale of the plot. Finally, the amplitude response of the two-pole filter designed by the equation-error method is shown overlaid in the figure. Note that the agreement is quite good near the peak which is what matters most. The interpolated peak frequency measured initially in the nonparametric spectral magnitude data can be used to fine-tune the pole-angles of the designed filter, thus rendering the equation-error method a technique for measuring only the peak bandwidth in this case. There are of course many, many techniques in the signal processing literature for measuring spectral peaks.

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Amplitude response peak measurement