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### Sampling frequency in bilinear transform when designing butterworth filter

Bilinear transform has a nonlinear frequency mapping $$\varOmega = \frac{2}{T}\tan{\frac{\omega}{2}}$$ Substituting $\varOmega = 1$ and $\omega = 0.5\pi$ into it and you can derive that $$T = 2$$ ...
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### How to design digital Butterworth filter and return its zeros, poles and gain

This can be designed in the following steps: Design a $N$-th order lowpass prototype of the analog Butterworth filter and you get an all-pole filter with poles  p_{a, n} = e^{j\pi(2n-1+N)/2N}, \ \ \...
• 2,628

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