Figure 6b: The received signal when first derivatives
of Gaussian signal used as transmitted signal
3.1 Signal processing
As explained in the first section, the shape and
bandwidth of transmitted signal changes during
passing the wall, hitting the target and returning to
the receiver antenna. Wall thickness and its
substance and distance between the human and
antenna also affect the received signal.
By using appropriate signal in transmitter, the
received signal can be predicted. As derivative of
transmitted signal, the bandwidth of the signal
changes and appears in receiver. Using wavelet
transform, because of predicting the occurred
changes like waveform and received signal
bandwidth, is helpful in background subtraction and
results appropriate output signal. Figure 7 shows
diagrams of final data resulted from signal
processing part which is human respiration periodic
signal.
The obtained results show that, Mayer and
Morlet wavelets give the best results by sending first
derivative of Gaussian signal in transmitter. Also
between these two wavelets, Mayer is closer to
received signal and has better results. In these
results, the background noise is completely omitted
and respiration signal with acceptable amplitude can
be observed (Figure 7a).
By sending the second derivative of Gaussian
signal, Mexican hat wavelet gives better and
acceptable output. By the way, Mayer wavelet
would be more suitable as the transmitted signal in
sending the second derivative of Gaussian signal
(Figure 7.b).
During simulation process, it could be
understood that the forth derivative of Gaussian
signal in transmitter would have the best results
using Morlet. For other derivatives (5, 6, 7), using
Coiflets, Symlets and Daubechies wavelets would
have better results which among them. Symlets
would be more appropriate for fifth derivative and
Daubechies would be more appropriate for sixth
derivative of Gaussian signal.
It can be concluded from the results that the
transmitted signal is formed by the transmitting
antenna and then it can be interpreted as the second
derivative of the transmitted signal at the receiver.
Considering this, the best results for the target can
be obtained by choosing appropriate wavelet.
In forward, after different simulations, it could
be observed that second derivative of Gaussian
signal would be the best choice for similar
environments. Also, if the distance between human
and antenna increase, using Daubechies wavelet
would be a better choice for extracting desired target
specifications. About walls with higher dielectric
constant, using second derivative of Gaussian signal
with Morlet wavelet would give the best results for
target specifications.
Figure 7a: the result of Meyer wavelet when first
derivatives of Gaussian signal used as transmitted signal
Figure 7b: the result of Mexican hat wavelet when
second derivatives of Gaussian signal used as transmitted
signal
(Vertical axis show the amplitude of breathing signal and
the horizontal axis show the repeat of this signal)