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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42 CHAPTER 2<br />
In Figure 2.13 we show an illustration <strong>of</strong> the sampling influences and aliasing<br />
situation when detecting a square wave <strong>with</strong> the 4-tap mechanism.<br />
input signal<br />
short-time<br />
integration<br />
ideal sampling<br />
Amplitude spectrum Phase spectrum<br />
S()<br />
f<br />
0.5<br />
ϕ()<br />
f<br />
()<br />
f<br />
S int<br />
DFT-amplitude spectrum<br />
<strong>of</strong> naturally sampled<br />
square wave<br />
⎛<br />
⎜<br />
f<br />
sinc 2π<br />
⋅<br />
⎝ 4f0<br />
0.5<br />
f 3<br />
0 f0<br />
0<br />
f 3<br />
0 f0<br />
0<br />
⎞<br />
⎟<br />
⎠<br />
F () samp f<br />
1<br />
0<br />
()<br />
f<br />
S samp<br />
int,<br />
0 f0<br />
f<br />
1<br />
f0 0 f 2 0 f 4 0 f 6<br />
0<br />
f<br />
4f0<br />
3ϕ0<br />
ϕ0<br />
f 3<br />
f0 0<br />
4f0 0 f 8 0 f 12 f<br />
aliasing<br />
f<br />
ϕ () int f<br />
3ϕ0<br />
ϕ0<br />
8f0 0 f 12<br />
f 3<br />
f0 0<br />
Figure 2.13 Aliasing for a square wave sampled <strong>with</strong> only four sampling points.<br />
Influence on amplitude and phase spectrum.<br />
f<br />
f<br />
f
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