Butterworth Low Pass Calculator
Expert Guide to Butterworth Low Pass Filters
Introduction & Importance
Butterworth low pass filters are essential in signal processing, offering a flat response in the passband and a maximally flat response in the stopband. They are widely used in audio, image, and communication systems.
How to Use This Calculator
- Enter the sampling frequency (Fs) and cutoff frequency (Fc).
- Select the order (N) of the filter.
- Click ‘Calculate’.
Formula & Methodology
The transfer function of a Butterworth low pass filter is given by:
H(s) = (1 / (1 + (s / (2 * π * Fc))^2N))
Where:
- s is the complex frequency variable (s = j * ω)
- Fc is the cutoff frequency
- N is the order of the filter
Real-World Examples
Coming soon…
Data & Statistics
| Order (N) | Maximum Ripple (dB) | Transition Width (Fs / N) |
|---|---|---|
| 1 | 3.01 | Fs |
| 2 | 1.59 | Fs / 2 |
| 3 | 0.81 | Fs / 3 |
Expert Tips
- Higher order filters offer better performance but increase complexity and cost.
- Butterworth filters are optimal for applications where a flat passband and a smooth transition to the stopband are required.
Interactive FAQ
What is the difference between a low pass and a high pass filter?
A low pass filter allows frequencies below the cutoff frequency to pass, while a high pass filter allows frequencies above the cutoff frequency to pass.
What is the effect of increasing the order of the filter?
Increasing the order of the filter improves the performance by reducing the transition width and maximum ripple, but increases the complexity and cost.
For more information, see the original paper by S. Butterworth and the Wikipedia article.