Neural Sync Active

Learning Objectives

Registry Synced

Learning Objectives

396 words

2 min read

Reading compass

Now · 1. Sampling & Quantization

Learning Objectives

Understand sampling, quantization, and Fourier analysis
Apply Z-transform and digital filters to speech
Analyze speech signals in frequency domain
Calculus (Fourier series/transform)
Week 1: Speech production

1. Sampling & Quantization

Sampling: Convert continuous time signal to discrete samples. Nyquist theorem: fs >= 2*fmax. Speech typically sampled at 8kHz (telephone) or 16kHz (wideband). Quantization: Convert continuous amplitude to discrete levels. More bits = higher quality. 16-bit PCM is standard for speech.

2. Fourier Analysis

Fourier Transform: Decompose signal into frequency components.

X(f) = \int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt

Short-Time Fourier Transform (STFT): Speech is non-stationary (changes over time). STFT applies Fourier transform to short windows (20-30ms) where speech is approximately stationary. Spectrogram: Visual representation of STFT. Time on x-axis, frequency on y-axis, intensity = energy (dB). Dark bands = formants.

3. Z-Transform & Digital Filters

Z-Transform:

X(z) = \sum_{n=-\infty}^{\infty} x[n] z^{-n}

Transfer Function: H(z) = Y(z)/X(z) - characterizes filter behavior Linear Prediction (LPC): Model speech sample as linear combination of past samples. Coefficients represent vocal tract shape. Used for formant estimation, speech coding, synthesis.

Q1: Why is speech analyzed in short frames (20-30ms)?

Speech is non-stationary (production changes over time). But over 20-30ms, speech is approximately stationary (vocal tract shape doesn't change significantly). Short frames enable frequency analysis of changing speech. Q2: What is the spectrogram and what information does it show?

Time-frequency representation. X-axis: time, Y-axis: frequency, Color: energy (dB). Reveals formants (vowel quality), harmonics (pitch), frication noise, silence, and transitions (consonant cues). Q3: What is pre-emphasis and why is it used?

High-pass filter applied before analysis. Boosts high frequencies to compensate for 6dB/octave roll-off in speech spectrum. Makes formant peaks more visible. Transfer function: H(z) = 1 - a*z^(-1), typically a=0.97. Q4: How does linear prediction model speech?

LPC models current sample as weighted sum of p past samples plus excitation. A(z) = 1 - sum(ak*z^(-k)). Coefficients ak encode vocal tract shape (all-pole filter). Order p typically 10-16 for speech. Q5: What is the Nyquist theorem and how does it apply to speech?

Sampling rate must be >= 2x maximum frequency. Telephone speech (8kHz sampling): max frequency 4kHz. Wideband speech (16kHz): max 8kHz. CD quality (44.1kHz): max 22kHz. Join Discord PreviousIntroduction to Speech ProcessingNextSpeech Analysis & Features