HilbertHRe:
Filter:
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HilbertHRe
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

The Hilbert Transform, returning the first 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. HilbertHRe is built with DelayN. Method *arConv also includes 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 real part of the Hilbert Transform.

.arConv

Return the real transform via convolution.

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 real part of the Hilbert Transform.

.calcCoeffs

Generate real coefficients.

Arguments:

size

The size of the kernel used for Hartley Phasing filtering.

Discussion:

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

Frequency response

Please review the discussion found here.

Examples

ar

arConv

[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.