HilbertPDN:

Filter: Extension

Applies the Hilbert Transform to an input signal. [1]

Source: Hilbert.sc

Offers the Hilbert and related transforms and analyses of an input signal via Weaver's *Second Method*,^{1} known as *Hartley Phasing*,^{2} expressed as a 12th-order Phase Differencing Network.^{3}

[1] this is a composite pseudo UGen. HilbertPDN is built with SOS. Method *arSSB also includes SinOsc.

The Hilbert Transform, returning two signals in *phase-quadrature*. Considered as a complex *analytic signal*,^{4} the first may be regarded as the *real* component and the second as the *imaginary*.

in |
The input signal to transform. |

mul |
Output will be multiplied by this value. |

add |
This value will be added to the output. |

An array of channels: `[real, imag]`

Rotate^{5} the phase of the input.

in |
The input signal. |

angle |
Rotation angle, in radians. |

mul |
Output will be multiplied by this value. |

add |
This value will be added to the output. |

Phase rotated input.

Single-Sideband Modulate^{6} (SSB) the input.

in |
The input signal. |

freq |
Frequency to shift by. May be positive or negative. |

mul |
Output will be multiplied by this value. |

add |
This value will be added to the output. |

SSB modulated input.

Analyze the *instantaneous amplitude* of the input.

in |
The input signal to analyze. |

mul |
Output will be multiplied by this value. |

add |
This value will be added to the output. |

*Instantaneous amplitude*.

Analyze the *instantaneous phase* of the input.

in |
The input signal to analyze. |

mul |
Output will be multiplied by this value. |

add |
This value will be added to the output. |

*Instantaneous phase*, in radians.

The both the `real`

& `imag`

outputs of HilbertPDN return an allpass magnitude response.

The both the `real`

& `imag`

outputs of HilbertPDN return a nonlinear phase response, where `imag`

is offset by `-pi/2`

radians with respect to `real`

.

[1] - Weaver, Donald. “A Third Method of Generation and Detection of Single-Sideband Signals.” Proceedings of the IRE, vol. 44, no. 12, 1956, pp. 1703–1705.

[2] - US Patent 1,666,206, Modulation System, April 17, 1928, United States Patent and Trademark Office.

[3] - B. Hutchins, “The Design of Wideband Analog 90° Phase Differencing Networks without Large Spread of Capacitor Values”, Electronotes, Special Issue G, No. 168, http://electronotes.netfirms.com/EN168-90degreePDN.PDF, accessed 2017-08-08.

[4] - Smith, J.O. “Analytic Signals and Hilbert Transform Filters”, in Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, Second Edition, https://ccrma.stanford.edu/~jos/st/Analytic_Signals_Hilbert_Transform.html, online book, 2007 edition, accessed 2017-08-08.

helpfile source: /Library/Application Support/SuperCollider/downloaded-quarks/Hilbert/HelpSource/Classes/HilbertPDN.schelp

link::Classes/HilbertPDN::

link::Classes/HilbertPDN::