Broad use of underground sensing led to development of a new signal processing algorithms which can extract much more information about soil and underground objects physical characteristics. These algorithms require information about how specific attenuation is dependent upon frequency, about phase velocity of radio waves in soil or about signals phase structure in cases when underground objects are present or absent. This kind of information can be easily obtained when using probinging signal with stepped change of a carr ier frequency. Radar systems with this kind of sensing signals are called Stepped Frequency Continues Wave (SFCW) GPR.The classical approach to signal processing of SFCW GPR is to use inverse discrete Fourier transform (IDFT) to transform frequency domain function to time domain. The result is a synthesized time profile containing the target's reflection coefficient and delay time. The IDFT algorithm is a pulse compression filter which com presses the received time waveform to form the high-resolution synthesized time waveform. For multiple targets, the IDFT compresses the reflected time waveforms by coherently summ ing the voltages of each target into their respective time bin in the synthesized profile.Having quadrature signals on the exit of phase detector as time domain signal, we can apply direct Furr ier transformation to obtain a result in the frequency domain where frequency values will correspond to depth values.Directly after Furr ier transform we have a real and imaginary parts of a signal spectrum which can be transformed to amplitude and phase. As a result we have amplitude spectrum which characterizes underground objects reflectance coefficient dependency upon depth and phase spectrum which can be used to extract additional information about soil and underground objects properties.Comparing our approach with classical algorithm we were able to see that results are almost identical in amplitude spectrum but there are big differences in phase spectrum.Another challenge in SFCW GPR signal processing is to eliminate signals reflected from radar antenna and air-earth border in reflected signals package at each GPR sensing point. Considerably new RELAX algorithm can be used to estimate parameters of a few powerful signal harmonics which are mixed with several other less powerful harmonics and noise. We use RELAX method to extract signals reflected from GPR antenna and air-earth border (because they are much more powerful than signals reflected from underground objects) from GRP signal at each sensing point.The RELAX algorithm is detailed in this section for spectral estimation. In the presence of the zero-mean white Gaussian noise, the ML estimator requires solving the nonlinear least-squares fitting problem. The RELAX algorithm provides excellent initial conditions for the next new sinusoidal parameter estimation [18]: the estimate of a new sinusoidal component is postponed until the already determined ones are "good enough". The building block of the RELAX algorithm is to estimate one...
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