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57 lines
1.9 KiB
Go
57 lines
1.9 KiB
Go
// Copyright ©2024 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package transform
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import (
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"fmt"
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"math/cmplx"
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)
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func ExampleHilbert_AnalyticSignal() {
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// Samples is a set of real amplitudes that make up a signal.
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samples := []float64{1, 0, 2, 0, 4, 0, 2, 0}
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// Initialize a Hilbert transform and 'demodulate' to get the
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// analytic signal.
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// The result is the complex I/Q (In-Phase / Quadrature) demodulation
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// of the input signal.
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h := NewHilbert(len(samples))
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iqSamples := h.AnalyticSignal(nil, samples)
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// We can compute the instantaneous amplitude of the signal
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// (or 'envelope') using absolute value. Analyzing the envelope
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// is an easy way to measure changes in amplitude over time in a
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// signal.
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envelope := make([]float64, len(samples))
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for ind, iq := range iqSamples {
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envelope[ind] = cmplx.Abs(iq)
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}
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// We can also compute the instantaneous phase of each part of the
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// signal using the 4-quadrant arc-tangent. With multiple samples,
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// the instantaneous phase can be used to estimate instantaneous
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// frequency of a signal.
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phase := make([]float64, len(samples))
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for ind, iq := range iqSamples {
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phase[ind] = cmplx.Phase(iq)
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}
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for i, iq := range iqSamples {
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fmt.Printf("ind=%d -> I=%.4f, Q=%.4f, envelope=%.4f, phase=%.4f\n",
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i, real(iq), imag(iq), envelope[i], phase[i])
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}
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// Output:
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//
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// ind=0 -> I=1.0000, Q=0.0000, envelope=1.0000, phase=0.0000
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// ind=1 -> I=-0.0000, Q=-0.8107, envelope=0.8107, phase=-1.5708
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// ind=2 -> I=2.0000, Q=0.0000, envelope=2.0000, phase=0.0000
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// ind=3 -> I=-0.0000, Q=-1.3107, envelope=1.3107, phase=-1.5708
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// ind=4 -> I=4.0000, Q=0.0000, envelope=4.0000, phase=0.0000
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// ind=5 -> I=0.0000, Q=1.3107, envelope=1.3107, phase=1.5708
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// ind=6 -> I=2.0000, Q=0.0000, envelope=2.0000, phase=0.0000
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// ind=7 -> I=0.0000, Q=0.8107, envelope=0.8107, phase=1.5708
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}
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