Question 1

What is the difference between Butterworth and Chebyshev Type I filters?

Accepted Answer

A Butterworth filter has a maximally flat passband magnitude response with no ripple, providing the smoothest possible rolloff. A Chebyshev Type I filter allows equiripple in the passband to achieve a steeper rolloff than Butterworth at the same filter order. Use Butterworth when passband flatness is critical; use Chebyshev when sharper stopband rejection is needed.

Question 2

What is the bilinear transform used in IIR filter design?

Accepted Answer

The bilinear transform converts an analog prototype filter to a digital filter using the mapping s = (2/T)·(z−1)/(z+1). It maps the entire analog frequency axis (−∞ to +∞) onto the digital unit circle, eliminating aliasing. However, it introduces a nonlinear frequency warping, so the analog cutoff frequency must be pre-warped to compensate before the transformation.

Question 3

How does increasing the filter order affect performance?

Accepted Answer

Increasing the filter order N makes the transition from passband to stopband steeper. A Butterworth filter rolls off at −20N dB/decade. Higher orders provide better stopband attenuation at the cost of increased computational load, greater phase nonlinearity, larger group delay, and potentially reduced numerical stability. Orders 4–8 are common in practice.

Question 4

What engineering applications use digital filters designed with this tool?

Accepted Answer

Typical applications include denoising vibration and acoustic sensor data, signal pre-processing in control systems, audio effect prototyping, structural health monitoring (SHM) acceleration data filtering, and biomedical signal conditioning (ECG, EEG). The displayed filter coefficients can be copied directly into Python (scipy.signal) or MATLAB for implementation.

Digital Filter Designer (IIR/FIR)

Theory