HilbertHIm:
Filter:
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HilbertHIm
ExtensionExtension

Applies the Imaginary 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

The Hilbert Transform, returning the second of two signals in phase-quadrature. Considered as a complex analytic signal, 3 the first may be regarded as the real component and the second as the imaginary.

[1] this is a composite pseudo UGen. HilbertHIm is built with Convolution2 and LocalBuf.

Class Methods

.ar

Arguments:

in

The input signal to transform.

size

The size of the kernel used for Hartley Phasing filtering.

mul

Output will be multiplied by this value.

add

This value will be added to the output.

Returns:

The imaginary part of the Hilbert Transform.

NOTE: The kernel used for Hartley Phasing filtering is windowed with the Signal: *kaiserWindow, where alpha is set to 1.

.calcCoeffs

Generate imaginary coefficients.

Arguments:

size

The size of the kernel used for Hartley Phasing filtering.

Discussion:

WARNING: To be deprecated! Use Signal *hilbert.imag instead.

Frequency response

Please review the discussion found here.

Examples

ar

[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] - 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.