HilbertHRe | 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 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

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 : HilbertHRe

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 {
    { // real
        HilbertHRe.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("Real; HilbertHRe; Impulse input", minval: -1, maxval: 1);
        }
        }
    );

0.5.wait;

{ // plot magnitude - real
        HilbertHRe.ar( // real
            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: "Real Magnitude Response",
                minval: plotDbMin,
                maxval: plotDbMax
            );
        }
        }
    );

}
)

/*
        TEST Hartley : HilbertHRe

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;

{ // real
    HilbertHRe.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("Real; HilbertHRe; Cosine input", minval: -1, maxval: 1);
    }
}
);
)

arConv

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 : HilbertHRe

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 {
    { // real
        HilbertHRe.arConv(
            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("Real; HilbertHRe; Impulse input", minval: -1, maxval: 1);
        }
        }
    );

0.5.wait;

{ // plot magnitude - real
        HilbertHRe.arConv( // real
            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: "Real Magnitude Response",
                minval: plotDbMin,
                maxval: plotDbMax
            );
        }
        }
    );

}
)

/*
        TEST Hartley : HilbertHRe

single cosine cycle: period = size
*/

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

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

{ // real
    HilbertHRe.arConv(
        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("Real; HilbertHRe; Cosine input", minval: -1, maxval: 1);
    }
}
);
)

[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: HelpSource/Classes/HilbertHRe.schelp
link::Hilbert/Classes/HilbertHRe::

HilbertHReExtension

Description

Class Methods

.ar

Arguments:

Returns:

.arConv

Arguments:

Returns:

.calcCoeffs

Arguments:

Discussion:

Frequency response

Examples

ar

arConv

HilbertHRe
Extension