octavebw2bw

Convert octave bandwidth to linear bandwidth

Since R2026a

Syntax

cutoffsAnalog = octavebw2bw(N,fc)

[cutoffsAnalog,cutoffsDigital] = octavebw2bw(N,fc,SampleRate=fs)

Description

cutoffsAnalog = octavebw2bw(N,fc) converts octave bandwidths N and band center frequencies fc into linear analog cutoff frequencies cutoffsAnalog.

[cutoffsAnalog,cutoffsDigital] = octavebw2bw(N,fc,SampleRate=fs) returns the digital cutoff frequency cutoffsDigital when you specify a sample rate using SampleRate=fs.

Examples

Find Cutoff Frequencies from Octave Bandwidths

Convert a set of octave bands to their corresponding cutoff frequencies.

First, define the octave bandwidths (N) and the octave band center frequencies (fc).

N = [0.2 0.5 0.4];
fc = [3000 4000 2500];

Compute the analog cutoff frequencies (fcuta).

fcuta = octavebw2bw(N,fc)

fcuta = 2×3
103 ×

    2.7991    3.3636    2.1764
    3.2153    4.7568    2.8717

Provide a sample rate to additionally compute the digital cutoff frequencies (fcutd).

fs = 16000;
[fcuta,fcutd] = octavebw2bw(N,fc,SampleRate=16000)

fcuta = 2×3
103 ×

    2.7991    3.3636    2.1764
    3.2153    4.7568    2.8717

fcutd = 2×3
103 ×

    2.7957    3.3137    2.1692
    3.2114    4.6863    2.8622

Input Arguments

N — Octave bandwidth

positive scalar | positive valued vector

Octave bandwidths, specified as a 1-by-P positive-valued vector, where P is the number of filter designs. The octave bandwidth is the ratio of upper to lower limits of the bandwidth express as a power of two.

Data Types: single | double

fc — Center frequency

positive scalar (default) | positive valued vector

Center frequencies, specified as a 1-by-P positive-valued vector, where P is the number of filter designs.

Example: 1400.0

Data Types: single | double

fs — Sample rate

2 (default) | positive scalar

Sample rate, specified as a positive scalar in Hz. The default value is 2. fc must be in the range [0,fs/2].

Example: 16000.0

Data Types: single | double

Output Arguments

cutoffsAnalog — Analog cutoff frequencies

positive-valued matrix

Analog cutoff frequencies, returned as a 2-by-P positive-valued matrix.

Example: 5000.0

Data Types: single | double

cutoffsDigital — Digital cutoff frequencies

positive-valued matrix

Digital cutoff frequencies in Hz, returned as a 2-by-P positive-valued matrix.

Example: 5000.0

Data Types: single | double

Algorithms

This function outputs both analog and digital band cutoff frequencies.

• Analog cutoff frequencies depend on the quality factor Q derived from the octave bandwidth N by

  $$Q=\frac{\sqrt{2^N}}{2^N-1}.$$

  The lower and upper band analog cutoff frequencies, cutoffsAnalog, are obtained from

  $$\begin{array}{l}{f}_1=f_c(\sqrt{1+\frac{1}{4Q^2}}-\frac{1}{2Q})\\ f_2=f_c(\sqrt{1+\frac{1}{4Q^2}}+\frac{1}{2Q})\end{array}$$

  where f_c is the band center frequency.

  Conversely, the octave bandwidth can be obtained from the ratio of f₂/f₁.

• Digital cutoff frequencies cutoffsDigital are computed iteratively following the algorithms presented in equations 58-61 of [1].

References

[1] Orfanidis, Sophocles, "High-Order Digital Parametric Equalizer Design", J. Audio Eng. Soc, 53, 2005.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2026a