Time Domain Methods in Speech Processing General Synthesis ...
Time Domain Methods in Speech Processing General Synthesis ...
Time Domain Methods in Speech Processing General Synthesis ...
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Short <strong>Time</strong> Energy and Magnitude—<br />
Rectangular W<strong>in</strong>dow<br />
E ˆn<br />
L=51 L=51<br />
L=101<br />
L=201<br />
L=401<br />
M ˆn<br />
L=101<br />
L=201<br />
L=401<br />
Short-<strong>Time</strong> Average ZC Rate<br />
zero cross<strong>in</strong>gs<br />
zero cross<strong>in</strong>g => successive samples<br />
have different algebraic signs<br />
• zero cross<strong>in</strong>g rate is a simple measure of the ‘frequency content’ of a<br />
signal—especially true for narrowband signals (e.g., s<strong>in</strong>usoids)<br />
• s<strong>in</strong>usoid at frequency F0 with sampl<strong>in</strong>g rate FS has FS/F0 samples per<br />
cycle with two zero cross<strong>in</strong>gs per cycle, giv<strong>in</strong>g an average zero<br />
cross<strong>in</strong>g rate of<br />
z1=(2) cross<strong>in</strong>gs/cycle x (F0 / FS ) cycles/sample<br />
z1=2F0 / FS cross<strong>in</strong>gs/sample (i.e., z1 proportional to F0 )<br />
zM=M (2F0 /FS ) cross<strong>in</strong>gs/(M samples)<br />
S<strong>in</strong>usoid Zero Cross<strong>in</strong>g Rates<br />
Assume the sampl<strong>in</strong>g rate is FS<br />
= 10, 000 Hz<br />
1. F0 = 100 Hz s<strong>in</strong>usoid has FS/ F0<br />
= 10, 000 / 100 = 100 samples/cycle;<br />
or z1 = 2 / 100 cross<strong>in</strong>gs/sample, or z100<br />
= 2 / 100 * 100 =<br />
2 cross<strong>in</strong>gs/10 msec <strong>in</strong>terval<br />
2. F0 = 1000 Hz s<strong>in</strong>usoid<br />
has FS/ F0=<br />
10, 000 / 1000 = 10 samples/cycle;<br />
or z1 = 2 / 10 cross<strong>in</strong>gs/sample, or z100<br />
= 2 / 10 * 100 =<br />
20 cross<strong>in</strong>gs/10 msec <strong>in</strong>terval<br />
3. F0 = 5000 Hz s<strong>in</strong>usoid has FS/ F0<br />
= 10, 000 / 5000 = 2 samples/cycle;<br />
or z1 = 2/ 2 cross<strong>in</strong>gs/sample,<br />
or z100<br />
= 2/ 2* 100=<br />
100 cross<strong>in</strong>gs/10 msec <strong>in</strong>terval<br />
31<br />
33<br />
35<br />
Short <strong>Time</strong> Energy and Magnitude—Hamm<strong>in</strong>g<br />
W<strong>in</strong>dow<br />
E ˆn<br />
L=51<br />
L=101<br />
L=201<br />
L=401<br />
M ˆn<br />
L=51<br />
L=101<br />
L=201<br />
L=401<br />
Short-<strong>Time</strong> Average ZC Rate<br />
Zero Cross<strong>in</strong>g for S<strong>in</strong>usoids<br />
1<br />
0.5<br />
0<br />
-0.5<br />
-1<br />
0 50 100 150 200<br />
1.5<br />
1<br />
0.5<br />
0<br />
offset:0.75, 100 Hz s<strong>in</strong>ewave, ZC:9, offset s<strong>in</strong>ewave, ZC:8<br />
Offset=0.75<br />
0 50 100 150 200<br />
100 Hz s<strong>in</strong>ewave<br />
100 Hz s<strong>in</strong>ewave with dc offset<br />
32<br />
34<br />
ZC=9<br />
ZC=8<br />
36<br />
6