EC05 · Sem 5 · Digital signal processing

IIR Butterworth filter

Aim: Design an IIR Butterworth filter with the bilinear transform and compare with FIR.

🧪 Live simulation🧊 Real-time 3D bench⚠ Simulated values, not physical measurements

🔬 Virtual lab

Starting the lab…

📘 Theory

IIR filters reuse past outputs (feedback), so a few coefficients give a steep roll-off. The bilinear transform maps an analog Butterworth prototype to digital with frequency pre-warping; the response is maximally flat in the pass band.

|H(f)| = 1/√(1 + (f/fc)^(2N)) · s = 2fs·(z − 1)/(z + 1)

🧰 Apparatus (virtual)

Noisy signal
IIR design tool (order 1–8)

📝 Procedure

Select IIR and order 4
Check the gain at the cut-off is −3 dB
Raise the order and see −20 dB/decade per order
Compare the computation with a FIR of similar sharpness

Observations and result (kept on this device)

🎤 Viva questions

What is the roll-off of a 4th-order Butterworth

80 dB per decade.

What is the main drawback of IIR filters

Non-linear phase and the possibility of instability.

🛡️ Safety

Virtual lab. With real RF equipment, respect exposure limits, never transmit without a licence, and keep antennas away from people.