Moving Average Filter Bandwidth
f3dB ≈ 0.443 × fs / N
Quick answer
This calculator solves f_3dB ≈ 0.443 × fs / N for −3 dB Frequency. With Sample Rate 2.2 kHz, Window Size 0.5, the result is 1.949 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | −3 dB Frequency | Hz | Hz, kHz, MHz, GHz |
| fs | Sample Rate | Hz | Hz, kHz, MHz, GHz |
| N | Window Size | — | — |
Step by step
- 1. What you know: Sample Rate 2.2 kHz, Window Size 0.5
- 2. The relation: f_3dB ≈ 0.443 × fs / N
- 3. Substitute: fs = 2.2 kHz, N = 0.5
- 4. Result: −3 dB Frequency = 1.949 kHz
Worked examples
Minimum range
Given: Sample Rate 11 Hz, Window Size 0.025
Result: −3 dB Frequency = 0.1949 kHz
Low range
Given: Sample Rate 110 Hz, Window Size 0.25
Result: −3 dB Frequency = 0.1949 kHz
Typical
Given: Sample Rate 2.2 kHz, Window Size 0.5
Result: −3 dB Frequency = 1.949 kHz
High range
Given: Sample Rate 44 kHz, Window Size 0.8
Result: −3 dB Frequency = 24.37 kHz
Maximum range
Given: Sample Rate 0.44 MHz, Window Size 8
Result: −3 dB Frequency = 24.37 kHz
Solving for each variable
Solve for −3 dB Frequency
Sample Rate 11 Hz, Window Size 0.025 → 0.1949 kHz
Solve for Sample Rate
−3 dB Frequency 5 Hz, Window Size 0.025 → 0.2822 Hz
Solve for Window Size
−3 dB Frequency 5 Hz, Sample Rate 11 Hz → 0.9746
How −3 dB Frequency changes with Sample Rate
| Sample Rate (input) | −3 dB Frequency (result) |
|---|---|
| 0.22 kHz | 0.1949 kHz |
| 0.55 kHz | 0.4873 kHz |
| 1.1 kHz | 0.9746 kHz |
| 1.65 kHz | 1.462 kHz |
| 2.2 kHz | 1.949 kHz |
| 3.3 kHz | 2.924 kHz |
| 4.4 kHz | 3.898 kHz |
| 8.8 kHz | 7.797 kHz |
| 15.4 kHz | 13.64 kHz |
| 22 kHz | 19.49 kHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 1949 |
| kHz | 1.949 |
| MHz | 0.001949 |
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<p><a href="https://vbatpower.com/formulas/moving-average-bw/">Moving Average Filter Bandwidth</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Moving Average Filter Bandwidth?
Use f_3dB ≈ 0.443 × fs / N. With Sample Rate 2.2 kHz, Window Size 0.5, −3 dB Frequency works out to 1.949 kHz.
What is the formula for Moving Average Filter Bandwidth?
The formula is f_3dB ≈ 0.443 × fs / N. The moving average filter is the simplest digital low-pass filter, computing the average of the last N samples.
How do you find Sample Rate when you know the other values?
Rearrange for Sample Rate: with −3 dB Frequency 5 Hz, Window Size 0.025, Sample Rate is 0.2822 Hz.
How do you find Window Size when you know the other values?
Rearrange for Window Size: with −3 dB Frequency 5 Hz, Sample Rate 11 Hz, Window Size is 0.9746.
What units does Moving Average Filter Bandwidth use?
−3 dB Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Filters formulas →Need more features?
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