hilbert

Builtin index · Signal processing

result = hilbert(x)

Input: x · Output: result

What it is

x is a length-N real vector.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = hilbert(x)`	`x` vectornot documented yet	`result` vector or CVec	Returns a length-N complex vector (`CVec`), the analytic signal `x + j*H[x]`. `abs(hilbert(x))` is `x`'s envelope; `imag(hilbert(x))` is the Hilbert transform of `x` itself.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

  envelope = abs(hilbert(am_signal))   # recovers an AM envelope

from numerics-dsp

How it works

hilbert(x) — the analytic signal x + j*H[x] (a CVec). abs(hilbert(x)) is x's envelope; imag(hilbert(x)) is the Hilbert transform of x itself.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.