1 Introduction
2 Modeling of human target echo
R
0
|
r
1
|
r
2
|
ω
1
|
ω
2
|
r
|
τ
|
---|---|---|---|---|---|---|
10 m | 5.5 mm | 0.9 mm | 0.24 Hz | 1.2 Hz | 0.25 cm | 0 s |
3 Time-frequency filtering separation algorithm
3.1 Time-frequency transformation
Carrier frequency, f
c
| Time, T
p
| Sampling frequency, f
s
| Frequency point, N
| Window, h
|
---|---|---|---|---|
220 GHz | 16 s | 512 Hz | 512 | Hamming |
3.2 Estimation of instantaneous frequency
3.3 Time-frequency filtering
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Evaluate IF—Using the algorithm mentioned above to estimate the instantaneous frequency of multi-component signal, it should be estimated in sequence by the signal power in the time-frequency domain.1.Evaluate the instantaneous frequency of all components, \( {\widehat{\omega}}_i(n), \) i = 1 corresponding to the highest signal component.2.Set the neighborhood region of \( {\widehat{\omega}}_i(n),\;\left[{\widehat{\omega}}_i(n)-\delta, {\widehat{\omega}}_i(n)+\delta \right] \) to zero-value, where δ is the zero region around the instantaneous frequency, forming a new time-frequency representation by B distribution method again.3.Repeat these two steps to estimate the instantaneous frequency corresponding to all signal components.
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Construct TFF—Time-frequency filter can be constructed based on the instantaneous frequency curve acquired by the steps above to separate the signal components.1.Choosing the suitable bandwidth based on the estimated instantaneous frequency to design the masking function C i(n,ω) [24],$$ {C}_i\left(n,\omega \right)=\left\{\begin{array}{c}\hfill 1,\hfill \\ {}\hfill 0,\hfill \end{array}\right.\begin{array}{c}\hfill k\in \left[{\widehat{\omega}}_i(n)-B(n)/2,{\widehat{\omega}}_i(n)+B(n)/2\right]\hfill \\ {}\hfill \mathrm{others}\hfill \end{array}, $$(14)in which \( {\widehat{\omega}}_i(n) \) is the instantaneous frequency evaluated and B(n) is the bandwidth of the masking region which is either time varying or constant. In this paper, we choose B(n) = 8.2.The time-frequency data BD i (n,ω) can be obtained by multiplying the time-frequency of the original signal BD(n,w) with the masking function C i (n,ω).3.The m-D signals can be obtained from the time-frequency data BD i (n,ω) inverse result.