Butterworth Low-Pass Filter Online Simulator

Butterworth Low-Pass Filter Simulator

Message Frequency (Hz):
Carrier Frequency (Hz):
Amplitude:
Sampling Frequency (Hz):
LPF Cutoff (Hz):
Butterworth Order:

Simulation Flow & Theory

This simulator performs DSB-SC (Double Sideband Suppressed Carrier) demodulation for a user-defined message signal and carrier. The steps are as follows:

1. Generate the message signal: m(t) = A_m cos(2π f_m t)
2. Generate the carrier: c(t) = cos(2π f_c t)
3. DSB-SC modulation: s(t) = m(t) · c(t)
4. Demodulation: multiply the modulated signal by the same carrier to get m(t) · cos²(2π f_c t)
5. Apply zero-phase Butterworth low-pass filter to remove the high-frequency term and retain the baseband message
6. Remove DC offset to center the signal around zero
7. Multiply by 2 to compensate the natural 1/2 scaling from cos²(θ) = (1 + cos(2θ))/2

Butterworth Filter: A first-order low-pass Butterworth filter is applied using the difference equation:

y[n] = α·x[n] + (1-α)·y[n-1],
where α = ω_c / (ω_c + 1), ω_c = 2π f_c / F_s,
and F_s is the sampling frequency, f_c is the cutoff frequency.

To implement an N-th order Butterworth filter, we cascade the first-order filter N times. The zero-phase filtering is achieved by applying the filter forward and backward to remove phase distortion.