Enter your Filter Order, Cutoff Frequency, Sample Rate, and Filter Type into the Butterworth Filter Calculator to find your Normalized Frequency, along with secondary outputs like Phase Lag, Gain at Cutoff, and Roll-off Rate — everything you need to dial in a maximally flat frequency response without the manual math.
Normalized Frequency
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Phase Lag
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Gain at Cutoff
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Roll-off Rate
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A Butterworth filter is designed to have a maximally flat frequency response in the passband, meaning it has no ripples. It provides the smoothest possible magnitude response but has a gradual roll-off compared to other filter types.
Higher filter orders provide steeper roll-off rates (better selectivity) but introduce more phase lag and computational complexity. Each order adds approximately 6dB/octave to the roll-off rate.
Low-pass filters allow frequencies below the cutoff to pass through while attenuating higher frequencies. High-pass filters do the opposite, passing high frequencies and blocking low frequencies.
The cutoff frequency should be set based on your signal requirements. It's the -3dB point where the filter begins significant attenuation. Consider your signal bandwidth and the frequencies you want to preserve or remove.
The sample rate must be at least twice the highest frequency of interest (Nyquist theorem). Common rates are 44.1kHz for audio, 48kHz for professional audio, and higher rates for specialized applications.
Normalized frequency is the cutoff frequency divided by the Nyquist frequency (half the sample rate). It ranges from 0 to 1, where 1 represents the Nyquist frequency.
Phase lag introduces a time delay that varies with frequency. While Butterworth filters have smooth magnitude response, they introduce non-linear phase distortion that may affect time-sensitive applications.