Matched Filter Simulator

Interactive visualization of a template signal, noisy signal, and matched filter output using Plotly.

Simulation Controls

Signal Length

Noise Std Dev

Original vs Noisy Signal

Matched Filter Output

As you know, a matched filter maximizes the signal-to-noise ratio (SNR) in the presence of additive noise. Its internal operation is mathematically represented as the convolution of the received signal with a time-reversed (and conjugated, in the complex case) version of the known template signal. The matched filter output reaches its maximum at time 𝑡 = 𝑇 t=T, where 𝑇 T is the symbol duration (i.e., when the received signal aligns with the template). In a practical scenario, assume the matched filter has prior knowledge of the pulse shape (e.g., BPSK pulse shaping) and the symbol duration. At the receiver, the matched filter processes the received signal by convolving it with the known BPSK pulse shape. The output is then sampled at the symbol intervals. If the transmitted symbol is 1, the matched filter output produces a peak (maximum value) within the corresponding symbol interval. A decision threshold is then applied to determine whether the transmitted symbol was 0 or 1, and this process continues for subsequent symbols.