HilbertHIm | SuperCollider 3.13.0 Help

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

HilbertHIm.ar(in, size: 2048, mul: 1.0, add: 0.0)

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.

HilbertHIm.calcCoeffs(size)

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.

Inherited class methods

Instance Methods

Inherited instance methods

Examples

ar

FFT analysis functions

NOTE: FFT returns linear frequency

*/
(
~calcMag = { arg kernel;

var fftResponse, fftMag;

// FFT analysis here!
    fftResponse = fft(
        kernel.as(Signal),
        Signal.newClear(kernel.size),
        Signal.fftCosTable(kernel.size)
    );

// find (& trim magnitude)
    fftMag = fftResponse.magnitude;
    fftMag = fftMag.copyFromStart((kernel.size/2).asInteger);

fftMag;
};
)

/*
        TEST Hartley : HilbertHIm

Impulse Response
*/
(
var size, dur, freq;
var overSample, start;
var plotDbMin, plotDbMax;

// kernel size
size = 2048;

overSample = 2;

// plot params
plotDbMin = -60.0;
plotDbMax = 6.0;

start = size - s.options.blockSize;  // offset - for kernel normalized to sample delay

dur = size / s.sampleRate;  // in seconds
freq = dur.reciprocal;

fork {
    { // imaginary
        HilbertHIm.ar(
            Impulse.ar(freq), // imulse test, one pulse over fftbuffer size
        size: size);
    }.loadToFloatArray(overSample * dur, s, {
        |arr|
        defer {
            arr = arr.copyRange(start, start+size-1);
            arr.plot("Imaginary; HilbertHIm; Impulse input", minval: -1, maxval: 1);
        }
        }
    );

0.5.wait;

{ // plot magnitude - imaginary
        HilbertHIm.ar( // imaginary
            Impulse.ar(freq), // imulse test, one pulse over fftbuffer size
        size: size);
    }.loadToFloatArray(overSample * dur, s, {
        |arr|
        defer {
            arr = arr.copyRange(start, start+size-1);
            ~calcMag.value(arr).ampdb.plot(
                name: "Imaginary Magnitude Response",
                minval: plotDbMin,
                maxval: plotDbMax
            );
        }
        }
    );

}
)

/*
        TEST Hartley : HilbertHIm

single cosine cycle: period = size
*/

(
var size, dur, freq;
var overSample, start;

size = 2048;
overSample = 4;
// plot: jump to the 2nd cycle, to account for "warm up" of Im kernel
start = 2 * size + ((size/ 2).floor).asInt - s.options.blockSize;  // offset - to sync cycle, for kernel normalized to sample delay

dur = size / s.sampleRate;  // in seconds
freq = dur.reciprocal;

{ // imaginary
    HilbertHIm.ar(
        SinOsc.ar(freq, pi/2), // cosine test, one cycle over fftbuffer size
        size: size);
}.loadToFloatArray(overSample * dur, s, {
    |arr|
    defer {
        arr = arr.copyRange(start, start+size-1);
        arr.plot("Imaginary; HilbertHIm; Cosine input", minval: -1, maxval: 1);
    }
}
);
)

Frequency response

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] - 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/HilbertHIm.schelp
link::Classes/HilbertHIm::

HilbertHIm : Object Extension

HilbertHIm.ar(in, size: 2048, mul: 1.0, add: 0.0)

Arguments:

Returns:

HilbertHIm.calcCoeffs(size)

Arguments:

Discussion:

HilbertHIm : Object
Extension