tf — Create a SISO transfer-function object from numerator and denominator coefficient vectors.

tf(num, den) creates a scalar-input scalar-output transfer-function object from numeric numerator and denominator coefficient vectors. Coefficients follow MATLAB's polynomial convention: the first entry is the highest-order term and the last entry is the constant term.

Syntax

H = tf(num, den)
H = tf(num, den, Ts)
H = tf(num, den, 'Variable', variable)
H = tf(num, den, 'Ts', Ts)

• num and den are numeric scalar, row-vector, or column-vector coefficient inputs. Coefficients are stored using MATLAB's highest-order-term-first polynomial convention.
• Ts is an optional finite non-negative sample time. Positive sample times default the transfer-function variable to 'z' unless Variable is provided explicitly.
• Variable accepts 's', 'p', 'z', 'q', 'z^-1', or 'q^-1'. The denominator vector must contain at least one non-zero coefficient.

How tf works

• Accepts numeric scalar, row-vector, or column-vector numerator coefficients.
• Accepts numeric scalar, row-vector, or column-vector denominator coefficients.
• Normalizes stored numerator and denominator coefficients to row vectors on the returned tf object.
• Returns a lightweight object whose class name is tf.
• Stores Numerator, Denominator, Variable, Ts, InputDelay, and OutputDelay properties on the object.
• Uses continuous-time defaults: Variable is 's' and Ts is 0.
• tf(num, den, Ts) stores a finite non-negative sample time and defaults Variable to 'z'.
• tf(num, den, 'Variable', variable) accepts variable values 's', 'p', 'z', 'q', 'z^-1', and 'q^-1'.
• tf(num, den, 'Ts', Ts) or tf(num, den, 'SampleTime', Ts) stores a finite non-negative sample time.
• Complex coefficients are accepted and stored as complex row vectors.
• Logical and integer coefficients are promoted to double precision.

GPU memory and residency

tf is a host-side object constructor. gpuArray coefficient inputs are gathered before object construction, and the returned transfer-function object does not live on the GPU.

Examples

Creating a first-order continuous-time transfer function

H = tf(20, [1 5]);
class(H)

Expected output:

ans = "tf"

Creating a second-order transfer function

H = tf([1 2], [1 3 2]);
H.Numerator
H.Denominator

Expected output:

H.Numerator = [1 2]
H.Denominator = [1 3 2]

Creating a discrete-time transfer function

H = tf(1, [1 -0.5], 0.1);
H.Variable
H.Ts

Expected output:

H.Variable = 'z'
H.Ts = 0.1

Selecting the polynomial variable

H = tf([1 0], [1 2 1], 'Variable', 'p');
H.Variable

Expected output:

H.Variable = 'p'

How RunMat validates tf

tf validates coefficient shapes, finite numeric values, supported variable names, and sample-time constraints before constructing the host-side transfer-function object. Unit and integration tests cover continuous and discrete constructors, row normalization, option parsing, and invalid denominator or matrix coefficient inputs.

• Implementation: `crates/runmat-runtime/src/builtins/control/tf.rs`

See Correctness & Trust for the full methodology and coverage table.

FAQ

Does tf evaluate the transfer function at frequency points?

No. This implementation only constructs the transfer-function object. Frequency-response helpers such as bode, freqresp, and evalfr are separate Control System Toolbox functions.

Does tf support MIMO transfer functions?

Not yet. This implementation supports scalar-input scalar-output systems created from numeric coefficient vectors.

Does tf implement step, impulse, or bode?

No. Those functions are not part of this builtin.

Can I pass matrices of coefficients?

No. Numerator and denominator inputs must be scalars or vectors.

Can the denominator be all zeros?

No. The denominator coefficient vector must contain at least one non-zero value.

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how tf works, line by line, in Rust.

• View tf.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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