Learning Objectives

• Extract MFCC features for speech recognition
• Analyze pitch, formants, and energy
• Understand cepstral analysis
• Week 2: Fourier analysis, filtering
• Understanding of frequency domain

1. Short-Term Analysis

• Frame size: 20-30ms (320-480 samples at 16kHz)
• Frame shift: 10ms (160 samples at 16kHz)
• Window function: Hamming window (reduces spectral leakage)

2. Mel-Frequency Cepstral Coefficients (MFCCs)

1. Pre-emphasis (boost high frequencies)
2. Frame blocking and windowing
3. Compute power spectrum (FFT)
4. Apply Mel filterbank (triangular filters spaced on Mel scale)
5. Log compression of filterbank energies
6. Discrete Cosine Transform (DCT) -> MFCCs Mel Scale: Perceptually motivated frequency scale.

3. Pitch (Fundamental Frequency F0)

• Typical F0: Male ~100-150 Hz, Female ~180-250 Hz, Children ~250-400 Hz
• Pitch detection: Autocorrelation, cepstral method, YIN algorithm

4. Energy & Zero-Crossing Rate

Q1: What are MFCCs and why are they effective for speech recognition?

MFCCs represent the spectral envelope in a compact, perceptually relevant form. They capture: vocal tract shape (formants), are robust to noise, decorrelated (DCT), and based on human hearing (Mel scale). Q2: What is the Mel scale and why is it used?

Psychophysical scale of perceived pitch. Human hearing has better frequency resolution at low frequencies. Mel scale approximates this: linear below 1kHz, logarithmic above. Filterbank has more filters at low frequencies. Q3: How is pitch (F0) estimated from speech?

Autocorrelation method: compute correlation of signal with itself at different lags. Peak at lag corresponding to pitch period. Cepstral method: peak in cepstrum at pitch period (quefrency). YIN algorithm: cumulative mean normalized difference function. Q4: What features distinguish voiced from unvoiced sounds?

Voiced: high energy, low ZCR, clear pitch, periodic waveform, strong formants. Unvoiced: low energy, high ZCR, no pitch, noise-like, flat spectrum. Q5: What are delta and delta-delta features?

First and second derivatives of MFCCs (velocity and acceleration). Capture temporal dynamics (how features change over time). Essential for good recognition accuracy. Deltas: difference between adjacent frames. Delta-deltas: difference of deltas. Q6: Write Python to extract MFCCs using librosa:

python
Run Inline
import librosa
# Load audio
y, sr = librosa.load('speech.wav', sr=16000)
# Extract 13 MFCCs
mfccs = librosa.feature.mfcc(y=y, sr=sr, n_mfcc=13, n_fft=512, hop_length=160)
# mfccs shape: (13, num_frames)