hilbert — Construct analytic signals with the Hilbert transform.
z = hilbert(x) returns the analytic signal associated with x. For complex single/double input, the imaginary part is ignored before the transform. Integer/logical signal data, typed or logical lengths, zero or empty lengths, and inputs beyond matrices are RunMat extensions.
Syntax
z = hilbert(x)
z = hilbert(x, N)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
x | NumericArray | Yes | — | Real-valued signal vector, matrix, or N-D array. |
N | NumericScalar | No | [] | FFT length along the first non-singleton dimension. |
Returns
| Name | Type | Description |
|---|---|---|
z | NumericArray | Analytic signal with real part equal to the input signal. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:hilbert:ArgCount | More than two input arguments are supplied. | hilbert: expected hilbert(X) or hilbert(X, N) |
RunMat:hilbert:InvalidLength | Length argument N is non-scalar, negative, non-finite, or fractional. | hilbert: invalid length argument |
RunMat:hilbert:InvalidInput | Input cannot be converted to a real numeric/logical signal. | hilbert: expected real numeric input |
RunMat:hilbert:Internal | FFT execution or tensor shaping fails internally. | hilbert: internal error |
How hilbert works
- Accepts documented single/double vectors and matrices; integer, logical, and N-D inputs require RunMat extension mode.
- Operates along the first non-singleton dimension, matching MATLAB's column-wise behavior for matrices and row-wise behavior for row vectors.
hilbert(x, N)pads with zeros or truncates along the transform dimension before constructing the analytic signal.- Returns complex scalar or complex tensor output; output shape follows the input shape except that the transform dimension becomes
Nwhen supplied. - The FFT-domain multiplier preserves DC and, for even lengths, Nyquist bins; positive-frequency bins are doubled and negative-frequency bins are zeroed.
- For complex single/double input, the imaginary component is ignored and the real component is transformed.
Does RunMat run hilbert on the GPU?
The WGPU provider computes FFT, analytic-signal weighting, and inverse FFT without gathering the source tensor to host.
The output handle is marked as complex-interleaved GPU storage for downstream resident complex operations.
If the provider hook is unavailable or the requested transform length is zero, the runtime gathers and uses the MATLAB-compatible host FFT implementation.
GPU memory and residency
hilbert keeps real GPU tensors resident when the active provider implements signal_hilbert, returning a complex-interleaved GPU tensor. An explicitly unsupported hook uses a non-destructive owner download and restores the complex result when the owner can preserve its precision; the source handle remains resident.
Examples
Analytic signal of a sampled cosine
x = [1 0 -1 0];
z = hilbert(x)Expected output:
z = [1.0000 + 0.0000i, 0.0000 + 1.0000i, -1.0000 + 0.0000i, 0.0000 - 1.0000i]Use Hilbert output for phase demodulation
fs = 8000;
t = 0:1/fs:0.1;
s = cos(2*pi*500*t + 2*sin(2*pi*20*t));
z = hilbert(s);
phase = unwrap(angle(z));Specify an FFT length
x = [1 0 -1 0];
z = hilbert(x, 8);
size(z)Expected output:
ans = [1 8]Operate down matrix columns
X = [1 0; 0 1; -1 0; 0 -1];
Z = hilbert(X);Using hilbert with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how hilbert changes the result.
Run a small hilbert example, explain the result, then change one input and compare the output.
FAQ
What does hilbert return?⌄
hilbert returns an analytic signal. Its real part is the input signal and its imaginary part is the Hilbert transform.
Which dimension is transformed?⌄
RunMat follows MATLAB's default: the first non-singleton dimension. For a column vector this is rows, for a row vector this is columns, and for a matrix this means each column is transformed independently.
How is the transform computed?⌄
RunMat computes an FFT, applies the standard one-sided analytic-signal multiplier, and then computes an inverse FFT.
Can I pass complex input?⌄
Yes for single and double input. MATLAB-compatible behavior ignores the input's imaginary component, transforms its real component, and returns the complex analytic signal. Typed complex-integer input is not supported.
Does hilbert run on GPU tensors?⌄
Yes. Providers with signal_hilbert support keep real GPU tensor inputs resident and return a complex GPU tensor. An explicitly unsupported hook downloads non-destructively through the input owner, computes on the host, and restores the result to that owner when its precision can be preserved.
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Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how hilbert is executed, line by line, in Rust.
- View the source for hilbert 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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