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Antigravity Agent 504fd5fb42 [G1-Sync] Manual knowledge update

2026-05-10 22:08:15 +09:00

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title

Signal Processing Foundations

매 한 줄

"매 signal processing 은 시간/공간 신호의 frequency / scale 분해와 그 위의 transform". Fourier (1822) 의 heat-equation series 부터 매 Cooley–Tukey FFT (1965), 그리고 2026 의 audio LLM (Whisper-large-v4, MoonShine), neural-vocoder (BigVGAN-2), brain–computer-interface (Neuralink N1) 까지의 backbone.

매 핵심

매 핵심 정리

Sampling theorem (Nyquist): bandwidth B 의 신호는 f_s ≥ 2B 면 perfect reconstruct.
Convolution theorem: time-domain convolution ↔ frequency-domain product.
Parseval: energy 는 time/freq 에서 동일.
Uncertainty: Δt · Δf ≥ 1/(4π) — 매 wavelet/STFT trade-off 의 근원.

매 Filters

FIR: stable, linear-phase 가능, 매 group-delay 일정.
IIR: 매 efficient 하지만 phase 비선형 + stability 주의.
Linear phase 의 필요: 매 audio crossover, ECG.
Adaptive (LMS, RLS, Kalman): 매 noise-cancelling, echo.

매 Transforms

DFT/FFT: 매 stationary 분석.
STFT: 매 short-time spectrum (mel-spec backbone).
Wavelet (DWT): 매 multiscale.
Hilbert: 매 instantaneous amplitude/phase.
Cepstrum: 매 pitch / formant.

매 응용

Audio gen: BigVGAN-2 vocoder 의 multi-scale STFT loss.
ASR: Whisper-large-v4 의 80-mel + log-magnitude.
EEG/BCI: bandpower in θ/α/β/γ.
Radar / lidar: matched filter, FMCW range-doppler.

💻 패턴

FFT-based PSD (Welch)

from scipy.signal import welch

def psd(x, fs):
    f, p = welch(x, fs=fs, nperseg=1024, noverlap=512, window="hann")
    return f, p

STFT + log-mel spectrogram

import torchaudio

mel = torchaudio.transforms.MelSpectrogram(
    sample_rate=16000, n_fft=400, hop_length=160, n_mels=80,
    f_min=0, f_max=8000, power=2.0,
)
log_mel = lambda wav: (mel(wav) + 1e-6).log()

FIR low-pass design (firwin)

from scipy.signal import firwin, filtfilt

def lpf(x, fs, cutoff_hz, taps=129):
    b = firwin(taps, cutoff_hz, fs=fs, window="hamming")
    return filtfilt(b, [1.0], x)

Butterworth IIR (zero-phase)

from scipy.signal import butter, sosfiltfilt

def bandpass(x, fs, lo, hi, order=4):
    sos = butter(order, [lo, hi], btype="band", fs=fs, output="sos")
    return sosfiltfilt(sos, x)

Wavelet denoise (PyWavelets)

import pywt, numpy as np

def wavelet_denoise(x, wavelet="db4", level=4):
    coeffs = pywt.wavedec(x, wavelet, level=level)
    sigma = np.median(np.abs(coeffs[-1])) / 0.6745
    thr = sigma * np.sqrt(2 * np.log(len(x)))
    coeffs[1:] = [pywt.threshold(c, thr, mode="soft") for c in coeffs[1:]]
    return pywt.waverec(coeffs, wavelet)[:len(x)]

Hilbert envelope

from scipy.signal import hilbert

def envelope(x):
    a = hilbert(x)
    return np.abs(a), np.unwrap(np.angle(a))

Resampling (polyphase)

from scipy.signal import resample_poly

def to_16k(x, fs):
    from math import gcd
    g = gcd(fs, 16000)
    return resample_poly(x, 16000 // g, fs // g)

CQT / chroma (music-domain)

import librosa  # 0.11.x
chroma = librosa.feature.chroma_cqt(y=wav, sr=sr, n_chroma=12, hop_length=512)

매 결정 기준

상황	Approach
Stationary spectrum	FFT / Welch PSD
Time-varying	STFT / Mel
Transient / multiscale	Wavelet
Pitch / formant	Cepstrum / autocorr
Linear-phase audio	FIR (filtfilt)
Real-time low-latency	IIR (biquad cascade)
Resampling	Polyphase (resample_poly)

기본값: ML feature 는 log-mel spectrogram, 분석은 Welch PSD, denoise 는 wavelet / RNNoise, real-time 은 SOS biquad.

🔗 Graph

부모: Linear-Algebra-Foundations · Probability-Theory-Foundations
변형: Information Theory · Signal in Noise
응용: Kalman-Filter-and-State-Tracking · Computer_Vision
Adjacent: Roughness (그래픽 및 물리) · Cross-Frequency Coupling (CFC)

🤖 LLM 활용

언제: audio/EEG pipeline, vocoder loss design, sensor preprocessing, time-series feature engineering. 언제 X: pure tabular data, NLP token streams (use sequence models directly).

❌ 안티패턴

Aliasing 무시: anti-alias LPF 없이 downsample → 매 spectral fold-back.
Window 의 leakage 미고려: rectangular window → sidelobe 심함, Hann/Blackman 사용.
filtfilt 를 real-time 에 사용: 매 non-causal — production 은 단방향 IIR + group-delay 보정.
dB 의 reference 누락: dBFS / dBSPL / dBm 명시 필수.

🧪 검증 / 검토

Verified (Oppenheim & Schafer "Discrete-Time Signal Processing" 3rd ed.; Mallat "Wavelet Tour" 3rd ed.; torchaudio docs 2.5).
신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — Nyquist/Parseval/uncertainty, FIR/IIR/wavelet/STFT patterns, 2026 audio-LLM context

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