Significance of Frame Size
- Need to ensure a sufficient amount of frames to capture non-stationary properties (not smoothed over)
- BUT taking a signal out of a signal can introduce information that was never there
- SO we must use overlapping frames
Overlapping Frames
- frame size N, number of samples per frame (or NT seconds)
- frame shift R, no of samples between successive frames
- frame rate 1/RT, frames per second fps
- T=1/fs is sample period
- fs = sample rate
- overlap = N-R
8000Hz = 8000 samples for 1 second of speech
Sampling Rate
Number of samples per second in Hz
Sample Period
1/sampling rate
Seconds per sample
Frame Length
- No. of samples per frame
- N = NT/T
Frame Shift
- No. of samples between starts of successive frames (R)
- R = 1/frT
Windowing Purpose
- Reduce edge discontinuities from framing, ensuring smooth transitions between frames
Window Functions
- Multiply each signal frame with a window function
- Most common are raised cosine window functions e.g. Hamming and Hanning
Energy
- Large in voiced speech e.g. open vowel sounds
- Short term energy is per block
- E = sum (squared sample values)
Normalised Energy
- E = 1/N sum (squared sample values)
Removes sensitivity based on no. of samples in analysis frame
Zero-Crossing Rate
- Large in unvoiced sounds e.g. p, ch
- No. of times the x-axis has been crossed
Speech/Non-speech detection
Simple version can be constructed using short-time energy (high in voiced speech) and zero-crossing rate (high in unvoiced speech)
Auto-Correlation
- Correlation with itself
- Emphasises periodicity, pitch is static within this
- Finds repeating patterns
- Basis for pitch detectors
- Expensive to compute as inner loop running for every sample
Auto-Correlation Function
r[k] = 1/N sum (s[i] * s[i+k])
Cepstral Analysis
- For separating vocal tract filter response from excitation spectrum (source)
- Frequency spectrum = vocal tract frequency response x excitation response
- Break into two components to make it more useful
Pitch Estimation with Cepstrum
Cepstrum - compute log spectrum of relationship
pseudo-frequency domain
Quefrency graph - find peak cepstral value in high quefrency components
Frame Rate
fr = 1/RT
