10.3 聲音演算法實戰總結#

取樣(1) → 時域特徵(2: 能量/ZCR/自相關)  ─┐
        → STFT(3) → 濾波器(4: FIR/IIR/EQ) ├→ 特徵(5: LPC/MFCC) → 模型(7,8,10)
        → 感知編碼(6: 遮蔽→量化)           │   → 增強/效果(9: 降噪/殘響/變速)
        → 端對端波形模型(10) ─────────────┘

import numpy as np

fs = 8000
t = np.arange(0, 3.0, 1/fs)
rng = np.random.default_rng(14)

# --- 場景合成：噪聲 + 殘響 + 兩段語音 ---
noise = 0.05*rng.normal(size=len(t))
clean = np.zeros(len(t))
for s, e in [(0.4, 1.4), (1.9, 2.8)]:
    idx = (t >= s) & (t < e)
    tt = t[idx] - s
    clean[idx] = 0.3*np.sin(2*np.pi*250*tt)*np.exp(-tt*2)*np.abs(np.sin(2*np.pi*3*tt))
rir = np.zeros(int(0.2*fs))
refl_t = [0.012, 0.031, 0.058, 0.091, 0.14]
for i, rt in enumerate(refl_t):
    rir[int(rt*fs)] = 0.6**i * (1 if i % 2 else -1)
wet = np.convolve(clean, rir)[:len(clean)]
y = wet + noise

# --- 步驟 1: VAD ---
F, H = 240, 80
n_fr = 1 + (len(y)-F)//H
E = np.array([10*np.log10(np.mean(y[i*H:i*H+F]**2)+1e-12) for i in range(n_fr)])
noise_db = np.median(E[:20])
act = E > noise_db + 10
# 合併段落
segs, st = [], None
for i, a in enumerate(act):
    if a and st is None: st = i
    if not a and st is not None:
        if i - st > 5: segs.append((st*H/fs, i*H/fs))
        st = None
if st is not None: segs.append((st*H/fs, n_fr*H/fs))

# --- 步驟 2: 維納降噪（僅對語音段做）---
N2, H2 = 256, 128
w = np.hanning(N2)
def wiener(seg):
    nfr = 1 + (len(seg)-N2)//H2
    Y = np.array([np.fft.rfft(seg[m*H2:m*H2+N2]*w) for m in range(nfr)])
    P = np.abs(Y)**2
    npsd = np.percentile(P, 20, axis=0) + 1e-12
    xi = np.maximum(P/npsd - 1, 0)
    G = np.clip(xi/(xi+1), 0.15, 1.0)
    out = np.zeros(len(seg)); ws = np.zeros(len(seg))
    for m in range(nfr):
        s = np.fft.irfft(Y[m]*G[m], N2)*w
        out[m*H2:m*H2+N2] += s; ws[m*H2:m*H2+N2] += w**2
    return out/np.maximum(ws, 1e-8)

def snr(a, b):
    return 10*np.log10(np.sum(a**2)/(np.sum(b**2)+1e-12))

print(f"偵測到 {len(segs)} 個語音段（真實 2 段）")
total_in = total_out = 0
processed = y.copy()
for s, e in segs:
    i0, i1 = int(s*fs), min(int(e*fs)+N2, len(y))
    den = wiener(y[i0:i1])
    processed[i0:i1] = den
    resid_in = y[i0:i1] - wet[i0:i1]     # 噪聲殘餘的代理
    resid_out = den - wet[i0:i1]
    total_in += np.sum(resid_in**2); total_out += np.sum(resid_out**2)

print(f"管線降噪量: {10*np.log10(total_in/total_out):+.1f} dB")
print(f"語音保留: 處理後訊號與乾淨訊號的相關 = "
      f"{np.corrcoef(processed[int(0.5*fs):int(1.3*fs)], clean[int(0.5*fs):int(1.3*fs)])[0,1]:.3f}")

# --- 步驟 3: 逐段 MFCC 區辨度（5.2 節函式的精神驗證）---
def mfcc_brief(seg, n_mfcc=8):
    seg = seg - seg.mean()
    S = np.abs(np.fft.rfft(seg*np.hanning(len(seg))))**2
    fb = np.linspace(0, len(S)-1, n_mfcc+2).astype(int)
    mel = np.array([S[fb[i]:fb[i+2]].sum() for i in range(1, n_mfcc+1)])
    c = np.cos(np.pi*np.outer(np.arange(n_mfcc), np.arange(n_mfcc)+0.5)/n_mfcc)
    return c @ np.log(mel + 1e-10)

v1 = mfcc_brief(y[int(0.5*fs):int(1.3*fs)])
v2 = mfcc_brief(y[int(2.0*fs):int(2.7*fs)])
print(f"兩段語音的 MFCC 距離 = {np.linalg.norm(v1-v2):.2f}（>0 表可區分內容差異）")

偵測到 2 個語音段（真實 2 段）
管線降噪量: +6.8 dB
語音保留: 處理後訊號與乾淨訊號的相關 = 0.987
兩段語音的 MFCC 距離 = 12.43（>0 表可區分內容差異）