Fourth-order Butterworth filtering

The CD-ROM that comes with this book contains four simulation file folders, one for each of the four simulators. Each folder contains the relevant simulation files for that particular simulator. Schematics in their native format are provided in all cases. The circuit names are provided in the appropriate section for that circuit. For example, Circuit 1, a fourth-order Butterworth low pass filter, lists the file names for that circuit as follows lp fltr (IsSpice), lpflt (Micro-Cap), lp fit (PSpice). Demonstration versions of each simulation tool set are also included. For SIMetrix both a PC version and a Linux version are included. 

The first filter in the chapter is one of the most popular. The schematic of the fourth-order Butterworth response low pass filter is shown in Fig. 3.1. The frequency response of the filter to an AC sweep is shown in Fig. 3.2. Note the flat response in the pass band and the stop band frequency of 100 kHz. 

Figure 3.1 Schematic of a fourth-order Butterworth low pass filter.

Figure 3.3 Breadboard configuration of fourth-order Butterworth filter.

Fourth-Order Butterworth High Pass Filter... 

Figure 3.7 Schematic of fourth-order Butterworth high pass filter. 

Shown in Fig. 8.6 is a fourth-order Butterworth low pass oscillator. Figure 8.7 is the square wave generated at node 10 and the resultant sine wave after filtering at node 3. The lab results are shown in Fig. 8.8. 

The thick line in Fig. 5.9 is the result of filtering the raw data in the forward and reverse directions using a fourth-order, low-pass Butterworth filter set at a cutoff frequency of 6 Hz (note that the front and back ends of the raw data were padded). This raises an interesting question, that is, how do we identify an appropriate cutoff frequency for the filter There are a number of methods that can be used to help select an appropriate cutoff frequency. A fast Fourier transform (FFT) can be used to... 

The magnitude functions are given in Table 4.7 for Butterworth LP prototype filters of second, third, and fourth order. 

Filter alignment is determined by the coefficients c, in the denominator polynomial of the transfer function. Table 4.9 provides the coefficients for Butterworth and Chebyshev alignment for second-, third-, and fourth-order filters. 

It is always advisible to filter out the noise, e.g., noise caused by rectification, by means of a 30 Hz fourth-order analog low-pass filter of the Butterworth type. This is also recommended if analog signals are to be AD converted. 

Finally, the 3D trajectories of the cutaneous markers were corrected by a low-pass filter (Butterworth, fourth-order, cut-off frequency of 5 Hz). A trajectory superposition procedure was performed to fill in the missing positions during experimental acquisition. 

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