Second Order Butterworth Low Pass Filter Calculator
Expert Guide to Second Order Butterworth Low Pass Filters
Introduction & Importance
Second order Butterworth low pass filters are essential in signal processing, providing a smooth roll-off and minimal phase shift. They are widely used in audio, image, and communication systems.
How to Use This Calculator
- Enter the cutoff frequency (fc) and sample frequency (fs).
- Select the order of the filter.
- Click ‘Calculate’.
Formula & Methodology
The transfer function of a second order Butterworth low pass filter is given by:
H(s) = 1 / (1 + (s/fc)^2)
Where fc is the cutoff frequency. The calculator uses this formula to compute the filter coefficients.
Real-World Examples
| fc (Hz) | fs (Hz) | Order | b0 | b1 | b2 | a1 | a2 |
|---|---|---|---|---|---|---|---|
| 1000 | 44100 | 2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
| 5000 | 48000 | 4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Data & Statistics
| fc (Hz) | fs (Hz) | Order | Ripple (dB) | Stopband Attenuation (dB) |
|---|---|---|---|---|
| 1000 | 44100 | 2 | 3.0103 | 20.88 |
| 5000 | 48000 | 4 | 1.7678 | 40.00 |
Expert Tips
- Higher order filters provide better attenuation but increase complexity.
- Always ensure fs > 2 * fc to avoid aliasing.
Interactive FAQ
What is the difference between a low pass and high pass filter?
A low pass filter allows low frequency signals to pass while attenuating high frequencies. A high pass filter does the opposite.
What is the Nyquist frequency?
The Nyquist frequency is half of the sample rate (fs/2). It is the highest frequency that can be represented without aliasing.