Moving Average Filter Bandwidth

Formula

Description

The moving average filter is the simplest digital low-pass filter, computing the average of the last N samples. Its −3 dB bandwidth is approximately 0.443 times the sample rate divided by the window size. Despite its simplicity, the moving average is optimal for reducing random noise while preserving step response — it has the fastest step response of any FIR filter for a given noise reduction. However, its frequency response has poor stopband attenuation (only 13 dB at the first null) and wide transition band, making it unsuitable for sharp frequency-selective filtering.

Variables

• f_3dB — Approximate −3 dB bandwidth (Hz)
• fs — Sampling frequency (Hz)
• N — Number of samples in the moving average window

Practical Notes

The exact first null occurs at fs/N. The 0.443 factor is an approximation based on the sinc-like frequency response. For better stopband attenuation, cascade multiple moving averages (CIC filter). A cascaded integrator-comb (CIC) filter with M stages has −3 dB bandwidth ≈ 0.443 × fs / (N × M^(1/(2M))). Moving averages are extremely efficient to implement: each output requires only one addition and one subtraction, regardless of N.