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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Frame-by-Frame Process<strong>in</strong>g <strong>in</strong> Successive W<strong>in</strong>dows<br />
• <strong>Speech</strong> is processed frame-by-frame <strong>in</strong> overlapp<strong>in</strong>g <strong>in</strong>tervals until entire<br />
region of speech is covered by at least one such frame<br />
• Results of analysis of <strong>in</strong>dividual frames used to derive model parameters <strong>in</strong><br />
some manner<br />
• Representation goes from time sample x[<br />
n],<br />
n = , 0,<br />
1,<br />
2,<br />
to parameter<br />
vector f[ nˆ], n= ˆ 0,1,2, where n is the time <strong>in</strong>dex and ˆn is the frame <strong>in</strong>dex.<br />
Generic Short-<strong>Time</strong> Process<strong>in</strong>g<br />
x[n] T(x[n])<br />
T( ) w[n]<br />
Q<br />
∞ ⎛ ⎞<br />
Qnˆ= ⎜ ∑ T([ x m]) w[ n−m] ⎟<br />
⎝ ⎠<br />
l<strong>in</strong>ear or non-l<strong>in</strong>ear<br />
transformation<br />
m=−∞ n= nˆ<br />
w<strong>in</strong>dow sequence<br />
(usually f<strong>in</strong>ite length)<br />
Qˆn<br />
• ˆn is a sequence of local weighted average<br />
values of the sequence T(x[n]) at time n= nˆ<br />
Computation of Short-<strong>Time</strong> Energy<br />
• w<strong>in</strong>dow jumps/slides across sequence of squared values, select<strong>in</strong>g <strong>in</strong>terval<br />
for process<strong>in</strong>g<br />
• what happens to Eˆn<br />
as sequence jumps by 2,4,8,...,L samples ( E ˆn is a lowpass<br />
function—so it can be decimated without lost of <strong>in</strong>formation; why is E ˆn lowpass?)<br />
• effects of decimation depend on L; if L is small, then E ˆn is a lot more variable<br />
than if L is large (w<strong>in</strong>dow bandwidth changes with L!)<br />
11<br />
7<br />
9<br />
Short-<strong>Time</strong> Signal Process<strong>in</strong>g<br />
Short-<strong>Time</strong> Parameter<br />
s[ n] Analysis Qˆn<br />
Estimation f [ nˆ<br />
]<br />
speech<br />
waveform<br />
alternate<br />
representation<br />
model<br />
parameter(s)<br />
Model Parameter(s):<br />
• speech/non-speech<br />
• voiced/unvoiced/background<br />
• pitch period (when voiced)<br />
• formants<br />
Short-<strong>Time</strong> Energy<br />
∞<br />
2<br />
E = ∑ x m<br />
m=−∞<br />
[ ]<br />
-- this is the long term def<strong>in</strong>ition of signal energy<br />
-- there is little or no utility of this def<strong>in</strong>ition for time-vary<strong>in</strong>g signals<br />
2 2<br />
[ ] = x [ nˆ − L+ 1]<br />
+ ... + x [ nˆ]<br />
Enˆ= ∑<br />
m=<br />
− + 1<br />
2<br />
x m<br />
ˆ n<br />
nˆ L<br />
-- short-time energy <strong>in</strong> vic<strong>in</strong>ity of time nˆ<br />
T( x) = x<br />
2<br />
wn [ ] = 1 0≤n≤L−1 = 0 otherwise<br />
Effects of W<strong>in</strong>dow<br />
Q = T( x[ n]) ∗w[<br />
n]<br />
= x′ [ n] ∗w[<br />
n]<br />
nˆ n= nˆ<br />
n= nˆ<br />
• w[n] serves as a lowpass filter on T(x[n]) which often has a lot of<br />
high frequencies (most non-l<strong>in</strong>earities <strong>in</strong>troduce significant high<br />
frequency energy—th<strong>in</strong>k of what (x[n] x[n]) does <strong>in</strong> frequency)<br />
• often we extend the def<strong>in</strong>ition of Qˆn<br />
to <strong>in</strong>clude a pre-filter<strong>in</strong>g term<br />
so that x[n] itself is filtered to a region of <strong>in</strong>terest<br />
xˆ[ n] L<strong>in</strong>ear x[n]<br />
T(x[n])<br />
Lowpass ˆn<br />
T( )<br />
Filter<br />
Filter, w[n]<br />
Q<br />
8<br />
10<br />
12<br />
2