Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 40. Butterworth Filters

Lowpass Butterworth filters are designed to have a magnitude response that is as flat as possible at low frequencies, and that decreases monotonically with increasing frequency, as shown in Figure 40.1. A lowpass Butterworth filter has a transfer function of the form shown in Math Box 40.1. Examination of this transfer function reveals that a Butterworth lowpass filter is an all-pole design that is completely specified by just two parameters—the number of poles, n, and the 3-dB cutoff frequency, ω_3dB. The number of poles is usually set to acheive a desired amount of attenuation, A_SB, at and above some specified stopband-edge frequency, ω_SB. This frequency and the amount of stopband attenuation are not direct specifications ...