Calculating the -3 dB cutoff frequencies - given center frequency and q factor bandwidth in octaves - filter octave 3 dB bandwidth calculator

• Calculation - Equalization - Filter •

Calculating the −3 dB cut-off frequencies f₁ and f₂
when center frequency f₀ and Q factor is given.
Bandwidth BW = f₂ − f₁= f₀/ Q and quality factor is Q factor
Parametric peak equalizer and notch (dip) equalizer

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Formula for the lower cutoff frequency:

Formula for the upper cutoff frequency:

Formulas mailed by Daniel Fournier

Formula for the Q factor:

Formula for the bandwidth:

A high filter quality means narrow-band filtering (notch), with a large Q factor.
This results in steep filter flanks with a small bandwidth.

A low filter quality means broad-band filtering, with a small Q factor.
This results in flat filter flanks with a large bandwidth.

Notice:
A low Q factor gives a broad band (wide) bandwidth or
a high Q factor gives a narrow band (small) bandwidth.

Q factor as a function of the bandwidth in octaves N (octave bandwidth)

Bandwidth in octaves N	Q factor
3.0 wide	0.404 low
2.0	0.667
1.0	1.414
2/3	2.145
1/2	2.871
1/3	4.318
1/6	8.651
1/12 small	17.310 high

Conversion: 'bandwidth per octave' N to quality factor Q
Interrelationship of 'octave bandwidth' N and the quality factor Q
Formulas for conversion of bandwidth in octaves to quality factor
Questions on "Parametric filter adjustment"
Conversion table Q to N and N to Q for parametric filters
Excel conversion - quality factor Q to bandwidth in octaves N
Filter slope (dB/oct) is not bandwidth
Calculating the center frequency from a given bandwidth

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