3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
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OPTICAL TOF RANGE MEASUREMENT 39<br />
input signal<br />
short-time<br />
integration<br />
ideal sampling<br />
DFT-amplitude spectrum<br />
<strong>of</strong> naturally sampled signal<br />
Amplitude spectrum Phase spectrum<br />
S()<br />
f<br />
0.5<br />
⎛<br />
⎜<br />
f<br />
sinc 2π<br />
⋅<br />
⎝ 4f0<br />
()<br />
f<br />
S int<br />
0 f0<br />
0 f 3<br />
0.5<br />
⎛ 1⎞<br />
⎜ ⎟<br />
⎝ π ⎠<br />
0 f0<br />
0 f 3<br />
S ()<br />
int, samp f<br />
0<br />
⎞<br />
⎟<br />
⎠<br />
⎛ 1 ⎞<br />
⎜ ⎟<br />
⎝ 3π<br />
⎠<br />
0<br />
f<br />
()<br />
f<br />
F samp<br />
1<br />
f<br />
0.5<br />
1<br />
f0 0 f 2 0 f 4 0 f 6<br />
0<br />
aliasing<br />
ϕ()<br />
f<br />
ϕ0<br />
3ϕ0<br />
ϕ0<br />
f0<br />
3 f0<br />
4f0 0 f 8 0 f 12 f<br />
f<br />
()<br />
ϕint<br />
f<br />
π<br />
π − 3ϕ0<br />
f 3<br />
f0 0<br />
3ϕ0<br />
− π<br />
− π<br />
4f0 0 f 8 0 f 12 f<br />
Figure 2.12 Aliasing for s( t)<br />
= cos(<br />
ω0t<br />
− ϕ0<br />
) + cos(<br />
3ω0t<br />
− 3ϕ0<br />
) sampled <strong>with</strong> only<br />
four sampling points. Influence on amplitude and phase spectrum.<br />
f<br />
f
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