HilbertPDNIm:

Filter: Extension

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

Source: Hilbert.sc

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

The Hilbert Transform, returning the second of 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*.

[1] this is a composite pseudo UGen. HilbertPDNIm is built with SOS.

in |
The input signal to transform. |

mul |
Output will be multiplied by this value. |

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

The imaginary part of the Hilbert Transform.

Please review the discussion found here.

[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/HilbertPDNIm.schelp

link::Classes/HilbertPDNIm::

link::Classes/HilbertPDNIm::