73 lines
2.2 KiB
Go
73 lines
2.2 KiB
Go
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// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
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// SPDX-License-Identifier: MIT
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package signal
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import (
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"math"
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"sourcedock.dev/petrbalvin/tensor/internal/base"
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"sourcedock.dev/petrbalvin/tensor/internal/core"
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)
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// AnalyticSignal builds the analytic signal z = x + i·H(x) of a real
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// series, where H is the Hilbert transform: the negative frequencies
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// are removed, the positive ones doubled and the DC and Nyquist bins
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// left alone, so z carries the instantaneous amplitude and phase of
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// the series. The Fourier definition treats the series as one period,
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// so it is exact for an integer number of tones and produces the
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// familiar edge swings on an aperiodic series, the same behaviour any
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// Fourier-domain filter shows there.
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func AnalyticSignal(data *core.Array) (*core.Array, error) {
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const name = "AnalyticSignal"
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if data.NDim() != 1 {
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return nil, base.Errf("%s: the series must be a vector, got shape %s", name, base.ShapeText(data.Shape()))
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}
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if data.Dtype() == core.Complex {
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return nil, base.Errf("%s: complex series are not supported", name)
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}
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n := data.Len()
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if n == 0 {
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return nil, base.Errf("%s: the series must not be empty", name)
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}
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spec, err := FFT(data)
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if err != nil {
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return nil, base.Errf("%s: %w", name, err)
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}
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bins := spec.RawComplexes()[:spec.Len()]
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half := (n + 1) / 2
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for k := range bins {
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switch {
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case k == 0 || (n%2 == 0 && k == n/2):
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// DC and, for even lengths, Nyquist: single-sided bins.
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case k < half:
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bins[k] *= 2
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default:
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bins[k] = 0
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}
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}
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out, err := IFFT(spec)
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if err != nil {
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return nil, base.Errf("%s: %w", name, err)
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}
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return out, nil
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}
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// Envelope returns the instantaneous amplitude of a series, the
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// modulus of its analytic signal. For a narrowband series this traces
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// the curve a peak detector would find, without the smoothing lag.
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func Envelope(data *core.Array) (*core.Array, error) {
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const name = "Envelope"
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z, err := AnalyticSignal(data)
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if err != nil {
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return nil, base.Errf("%s: %w", name, err)
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}
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bins := z.RawComplexes()[:z.Len()]
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out := core.New(core.Float, z.Len())
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vals := out.RawFloats()
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for i, c := range bins {
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vals[i] = math.Hypot(real(c), imag(c))
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}
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return out, nil
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}
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