1. Duration & Pitch Modification via WSOLA
Jyh-Shing Roger Jang (張智星)
CSIE Dept, National Taiwan University

2. Intro to WSOLA WSOLA Waveform Similarity OverLap and Add
A good way for duration & pitch modification in time domain

3. Naïve Method for Duration Modification
If duration ratio = 2, let’s duplicate frames directly:

4. Duration Ratio = 2 Zoom in the generate waveform  Not continuous
It is better to use OLA (OverLap & Add)

5. OverLap & Add (OLA) via Cross Fading
Quiz!
In practice, we usually use cross fading to make the waveform continuous when concatenating a frame.
Cross
fading

6. Example of Cross Fading
Given the following facts, what is the signal after OLA with cross fading?
Signal 1 = [ ]
Signal 2 = [ ]
Overlap = 3
Solution:
temp=linspace(0, 1, overlap+2);
upRamp=temp(2:end-1);
downRamp=1-upRamp;
Output = [[ ], [2 0 6].*downRamp+[8 6 8 ].*upRamp, [ ]]

7. Analysis and Synthesis
Usually we analyze a frame and synthesize it (put it into the output), with an overlap of 50% of the frame size. This is called the process of analysis and synthesis.

8. OLA Examples (1/3)
Duration ratio = 1, hop size = ½ frame size

9. OLA Examples (2/3)
Duration ratio = 2, hop size = ¼ of frame size

10. OLA Examples (3/3)
Duration ratio = 3, hop size=1/6 of frame size

11. Exact Formula for the Hop Size
If duration ratio is k, what is the exact hop size for the original signal with n frames?
This is the exact formula:
Quiz!

12. WSOLA OLA does not try to keep the structure of fundamental period
Use WSOLA to search for pitch-synchronized frames in the neighborhood
Demo
Try the selfdemo of wsola.m

13. WSOLA for Pitch Modification
Steps to modify the original pitch by Dp
Use duration ratio of 2^(Dp/12) to change duration by WSOLA
Resample the signals to have the original length
Demo
pitchShift.m in SAP Toolbox
Quiz!