buttord — Select the minimum Butterworth filter order.
buttord(Wp, Ws, Rp, Rs) computes the minimum Butterworth filter order and natural cutoff Wn that satisfy passband ripple Rp and stopband attenuation Rs. Digital frequencies use MATLAB's normalized convention where 1 is Nyquist; add 's' for analog rad/s designs.
Syntax
[n, Wn] = buttord(Wp, Ws, Rp, Rs)
[n, Wn] = buttord(Wp, Ws, Rp, Rs, 's')Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
Wp | NumericArray | Yes | — | Passband edge or two-element passband edge vector. |
Ws | NumericArray | Yes | — | Stopband edge or two-element stopband edge vector. |
Rp | NumericScalar | Yes | — | Maximum passband ripple in dB. |
Rs | NumericScalar | Yes | — | Minimum stopband attenuation in dB. |
Wp | NumericArray | Yes | — | Analog passband edge or edge pair in rad/s. |
Ws | NumericArray | Yes | — | Analog stopband edge or edge pair in rad/s. |
s | StringScalar | Yes | — | Analog-design selector. |
Returns
| Name | Type | Description |
|---|---|---|
n | NumericScalar | Minimum Butterworth filter order. |
Wn | NumericArray | Natural cutoff frequency or frequency pair for butter. |
Returned values from buttord depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:buttord:ArgCount | The argument count is outside supported forms. | buttord: expected buttord(Wp, Ws, Rp, Rs [, 's']) |
RunMat:buttord:InvalidFrequency | Passband or stopband edges are invalid. | buttord: invalid passband or stopband frequency |
RunMat:buttord:InvalidAttenuation | Ripple or attenuation values are invalid. | buttord: Rp and Rs must be positive finite scalars with Rs > Rp |
RunMat:buttord:InvalidOption | The optional selector is not supported. | buttord: optional selector must be 's' |
RunMat:buttord:TooManyOutputs | More than two output arguments are requested. | buttord: too many output arguments |
RunMat:buttord:Internal | Output tensor construction fails internally. | buttord: internal error |
How buttord works
[n, Wn] = buttord(Wp, Ws, Rp, Rs)returns a double scalar with an integral value fornand double cutoffWnfor direct use with the documented double-onlybutter(n, Wn)interface.- Scalar
WpandWsselect lowpass whenWp < Wsand highpass whenWp > Ws. - Two-element edge vectors select bandpass when the stopband encloses the passband and bandstop when the passband encloses the stopband.
- Digital inputs must be finite, positive, and less than 1. RunMat currently requires analog inputs to be finite and positive.
Rsmust be greater thanRp, and both values are specified in decibels.- Documented inputs are real
singleordouble. RunMat mode additionally admits independently gated typed-integer frequency and attenuation roles, logical roles, zero-imaginary complex frequency edges, and resident arguments; all cross explicit binary64 analysis boundaries and return host double values. - MATLAB documents infinite passband or stopband edges for analog designs. RunMat's shared order-selection validator currently rejects nonfinite edges, so that non-integer compatibility gap remains open.
Examples
Lowpass order selection
[n, Wn] = buttord(0.2, 0.3, 1, 40);
[b, a] = butter(n, Wn);Highpass order selection
[n, Wn] = buttord(0.5, 0.3, 1, 40);
[b, a] = butter(n, Wn, 'high');Bandpass order selection
[n, Wn] = buttord([0.3 0.5], [0.2 0.6], 1, 30);
[b, a] = butter(n, Wn, 'bandpass');Analog lowpass order selection
[n, Wn] = buttord(10, 20, 1, 40, 's');
[b, a] = butter(n, Wn, 's');Using buttord with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how buttord changes the result.
Run a small buttord example, explain the result, then change one input and compare the output.
FAQ
What should I pass to butter after buttord?⌄
Pass the returned n and Wn directly. For scalar highpass designs, also pass 'high'; for two-element bandpass or bandstop designs, pass 'bandpass' or 'stop' to match the edge layout.
Does buttord run on the GPU?⌄
The documented API lists code generation but no interactive gpuArray overload. In MATLAB-compatible mode RunMat rejects resident arguments before gather; RunMat mode gathers all four design roles and returns host double order/cutoff values.
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Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how buttord is executed, line by line, in Rust.
- View the source for buttord in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
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