Learning Objectives
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# 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 t...
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.
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: 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