written 2.3 years ago by | • modified 2.3 years ago |
Determine the order of a Butterworth low-pass filter satisfying the following specifications: fp=0.10 Hz fs=0.15 Hz αp=0.5 dB αs=15 dB;f=1 Hz
written 2.3 years ago by | • modified 2.3 years ago |
Determine the order of a Butterworth low-pass filter satisfying the following specifications: fp=0.10 Hz fs=0.15 Hz αp=0.5 dB αs=15 dB;f=1 Hz
written 2.3 years ago by |
Solution:
The type of transformation is not specified. Let us use bilinear transformation,
Ω2Ω1=2Ttanω222Ttanω12=21tan0.3π221tan0.2π2=1.0190.649=1.57
$ \begin{aligned} N & \geq \frac{1}{2} \frac{\log \left\{\left[\frac{1}{A_2^2}-1\right] /\left[\frac{1}{A_1^2}-1\right]\right\}}{\log \left(\frac{\Omega_2}{\Omega_1}\right)} \\\\ & \geq \frac{1}{2} \frac{\log \left\{\left[\frac{1}{0.177^2}-1\right] /\left[\frac{1}{0.944^2}-1\right]\right\}}{\log (1.57)} \\\\ & \geq 6.16 \approx 7\\ …