HilbertPDNRe:
Filter:
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HilbertPDNRe
ExtensionExtension

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

Description

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 first 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. HilbertPDNRe is built with SOS.

Class Methods

.ar

Arguments:

in

The input signal to transform.

mul

Output will be multiplied by this value.

add

This value will be added to the output.

Returns:

The real part of the Hilbert Transform.

Frequency response

Please review the discussion found here.

Examples

[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.