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| 1 | +"""Port of BloodFlowVelocity/perBeatSignalAnalysis.m.""" |
| 2 | + |
| 3 | +from __future__ import annotations |
| 4 | + |
| 5 | +from dataclasses import dataclass |
| 6 | + |
| 7 | +import numpy as np |
| 8 | + |
| 9 | +from ._signal_utils import next_power_of_two, normalize_cycle_boundaries |
| 10 | + |
| 11 | + |
| 12 | +@dataclass(frozen=True) |
| 13 | +class PerBeatSignalAnalysisResult: |
| 14 | + velocity_signal_per_beat: np.ndarray |
| 15 | + velocity_signal_per_beat_fft: np.ndarray |
| 16 | + velocity_signal_per_beat_band_limited: np.ndarray |
| 17 | + |
| 18 | + |
| 19 | +def _interpft_real(signal: np.ndarray, target_length: int) -> np.ndarray: |
| 20 | + source = np.asarray(signal, dtype=np.float64).reshape(-1) |
| 21 | + source_length = int(source.size) |
| 22 | + if source_length == 0: |
| 23 | + raise ValueError("interpft requires a non-empty signal.") |
| 24 | + if target_length <= 0: |
| 25 | + raise ValueError("interpft target_length must be positive.") |
| 26 | + if target_length == source_length: |
| 27 | + return source.copy() |
| 28 | + |
| 29 | + spectrum = np.fft.fft(source) |
| 30 | + resized = np.zeros(int(target_length), dtype=np.complex128) |
| 31 | + _copy_resized_spectrum(spectrum, resized, source_length) |
| 32 | + interpolated = np.fft.ifft(resized) * (float(target_length) / float(source_length)) |
| 33 | + return interpolated.real |
| 34 | + |
| 35 | + |
| 36 | +def _copy_resized_spectrum( |
| 37 | + spectrum: np.ndarray, |
| 38 | + resized: np.ndarray, |
| 39 | + source_length: int, |
| 40 | +) -> None: |
| 41 | + if source_length % 2 == 0: |
| 42 | + half = source_length // 2 |
| 43 | + resized[:half] = spectrum[:half] |
| 44 | + resized[-(source_length - half - 1) :] = spectrum[half + 1 :] |
| 45 | + resized[half] = spectrum[half] / 2.0 |
| 46 | + resized[resized.size - half] = spectrum[half] / 2.0 |
| 47 | + return |
| 48 | + |
| 49 | + pivot = source_length // 2 + 1 |
| 50 | + resized[:pivot] = spectrum[:pivot] |
| 51 | + resized[-(source_length // 2) :] = spectrum[pivot:] |
| 52 | + |
| 53 | + |
| 54 | +def per_beat_signal_analysis( |
| 55 | + signal, |
| 56 | + sys_idx_list, |
| 57 | + band_limited_signal_harmonic_count: int, |
| 58 | + *, |
| 59 | + index_base: int | None = None, |
| 60 | +) -> PerBeatSignalAnalysisResult: |
| 61 | + signal_array = np.asarray(signal, dtype=np.float64).reshape(-1) |
| 62 | + if signal_array.size == 0: |
| 63 | + raise ValueError("signal must contain at least one sample.") |
| 64 | + if band_limited_signal_harmonic_count < 1: |
| 65 | + raise ValueError("band_limited_signal_harmonic_count must be positive.") |
| 66 | + |
| 67 | + cycle_boundaries = normalize_cycle_boundaries( |
| 68 | + sys_idx_list, |
| 69 | + signal_array.size, |
| 70 | + index_base=index_base, |
| 71 | + ) |
| 72 | + return _analyze_cycles( |
| 73 | + signal_array, |
| 74 | + cycle_boundaries, |
| 75 | + int(band_limited_signal_harmonic_count), |
| 76 | + ) |
| 77 | + |
| 78 | + |
| 79 | +def _analyze_cycles( |
| 80 | + signal_array: np.ndarray, |
| 81 | + cycle_boundaries: np.ndarray, |
| 82 | + harmonic_count: int, |
| 83 | +) -> PerBeatSignalAnalysisResult: |
| 84 | + number_of_beats = int(cycle_boundaries.size - 1) |
| 85 | + n_fft = next_power_of_two(int(np.max(np.diff(cycle_boundaries)))) |
| 86 | + per_beat, per_beat_fft, band_limited = _empty_outputs(number_of_beats, n_fft) |
| 87 | + |
| 88 | + for beat_index in range(number_of_beats): |
| 89 | + start = int(cycle_boundaries[beat_index]) |
| 90 | + stop = int(cycle_boundaries[beat_index + 1]) + 1 |
| 91 | + beat_interp = _interpft_real(signal_array[start:stop], n_fft + 1)[:-1] |
| 92 | + beat_fft = np.fft.fft(beat_interp, n=n_fft) |
| 93 | + per_beat[beat_index, :] = beat_interp |
| 94 | + per_beat_fft[beat_index, :] = beat_fft |
| 95 | + band_limited[beat_index, :] = _band_limited_signal( |
| 96 | + beat_fft, |
| 97 | + n_fft, |
| 98 | + harmonic_count, |
| 99 | + ) |
| 100 | + |
| 101 | + return PerBeatSignalAnalysisResult(per_beat, per_beat_fft, band_limited) |
| 102 | + |
| 103 | + |
| 104 | +def _empty_outputs( |
| 105 | + number_of_beats: int, |
| 106 | + n_fft: int, |
| 107 | +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: |
| 108 | + per_beat = np.full((number_of_beats, n_fft), np.nan, dtype=np.float64) |
| 109 | + per_beat_fft = np.full((number_of_beats, n_fft), np.nan + 0j, dtype=np.complex128) |
| 110 | + band_limited = np.full((number_of_beats, n_fft), np.nan, dtype=np.float64) |
| 111 | + return per_beat, per_beat_fft, band_limited |
| 112 | + |
| 113 | + |
| 114 | +def _band_limited_signal( |
| 115 | + beat_fft: np.ndarray, |
| 116 | + n_fft: int, |
| 117 | + harmonic_count: int, |
| 118 | +) -> np.ndarray: |
| 119 | + count = min(int(harmonic_count), n_fft) |
| 120 | + band_limited_spectrum = beat_fft[:count].copy() * 2.0 |
| 121 | + band_limited_spectrum[0] = beat_fft[0] |
| 122 | + return np.abs(np.fft.ifft(band_limited_spectrum, n=n_fft)) |
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