A
Anonymous
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Ref: "Demodulator window widths" thread beginning 1 Feb 02.
Although PI's have usually been demodulated in the time domain, Fourier analysis is often talked about, and has actually been done in the past.
The technique I call "subharmonic analysis" probably corresponds to some kind of transform; which, however, I don't know the name of. It takes the basic idea of Fourier analysis and turns it upside down. From a computational standpoint, it is far simpler than conventional Fourier analysis. It readily scales to log form, facilitating its use in ground balancing and iron discrimination. However, unlike Fourier analysis, its potential for eliminating interfering signals is very limited.
Rather than go into a discussion of theory, I'll just describe an example of a system. This one happens to use direct sampled A/D conversion and demodulation; however, the same principles can be applied to systems using hardware demodulators.
Let's say we have a PI with a receive period totalling something greater than 160 microseconds. The sampling sequence is 0, 10, 20, 40, 80, and 160 microseconds. Each sample is subtracted at unity gain from the first sample to produce a demodulated signal. Earth field and DC offsets are cancelled.
The 10 us (software) "channel" is generally representative of target energy at 50 kHz, the 20 us at 25 kHz, etc. on out to 160 us being generally representative of energy at 3.1 kHz.
If the gain of each channel is made proportional to the time lag it represents, then to a very crude first approximation, signals from iron, iron minerals, and high-conductivity targets will tend to plot in a straight line. The actual plot will depend not only on target type, but the waveform of the transmit-flyback current, the pulse rep rate, and the delay prior to the first sample.
Things pretty much like this have been done strictly in the time domain. The difference is that in the time domain, the successive samples are taken as positive, and the last sample is subtracted to get earth field cancellation. In the proposed system, only the first sample is considered to be positive, and all the others are subtracted in their respective demodulated data channels.
So what's the advantage? Probably not a lot. It appears to be slightly better suited to discrimination, with low-conductivity targets dominating the response at high frequencies, and high-conductivity and iron and ground dominating at low frequencies. To get an all-metals signal, you'd sum the channels.
To provide mag-viscosity compensation for each signal, you'd subtract from each channel the following channel in a (presumptively) fixed proportion. Compared to a strictly time-domain approach, this provides more accurate compensation of mag-viscosity by making it less dependent on the size distribution of thermal superparamagnetic particles and on the energy distribution of lattice defects of different character in multidomain particles.
--Dave J.
Although PI's have usually been demodulated in the time domain, Fourier analysis is often talked about, and has actually been done in the past.
The technique I call "subharmonic analysis" probably corresponds to some kind of transform; which, however, I don't know the name of. It takes the basic idea of Fourier analysis and turns it upside down. From a computational standpoint, it is far simpler than conventional Fourier analysis. It readily scales to log form, facilitating its use in ground balancing and iron discrimination. However, unlike Fourier analysis, its potential for eliminating interfering signals is very limited.
Rather than go into a discussion of theory, I'll just describe an example of a system. This one happens to use direct sampled A/D conversion and demodulation; however, the same principles can be applied to systems using hardware demodulators.
Let's say we have a PI with a receive period totalling something greater than 160 microseconds. The sampling sequence is 0, 10, 20, 40, 80, and 160 microseconds. Each sample is subtracted at unity gain from the first sample to produce a demodulated signal. Earth field and DC offsets are cancelled.
The 10 us (software) "channel" is generally representative of target energy at 50 kHz, the 20 us at 25 kHz, etc. on out to 160 us being generally representative of energy at 3.1 kHz.
If the gain of each channel is made proportional to the time lag it represents, then to a very crude first approximation, signals from iron, iron minerals, and high-conductivity targets will tend to plot in a straight line. The actual plot will depend not only on target type, but the waveform of the transmit-flyback current, the pulse rep rate, and the delay prior to the first sample.
Things pretty much like this have been done strictly in the time domain. The difference is that in the time domain, the successive samples are taken as positive, and the last sample is subtracted to get earth field cancellation. In the proposed system, only the first sample is considered to be positive, and all the others are subtracted in their respective demodulated data channels.
So what's the advantage? Probably not a lot. It appears to be slightly better suited to discrimination, with low-conductivity targets dominating the response at high frequencies, and high-conductivity and iron and ground dominating at low frequencies. To get an all-metals signal, you'd sum the channels.
To provide mag-viscosity compensation for each signal, you'd subtract from each channel the following channel in a (presumptively) fixed proportion. Compared to a strictly time-domain approach, this provides more accurate compensation of mag-viscosity by making it less dependent on the size distribution of thermal superparamagnetic particles and on the energy distribution of lattice defects of different character in multidomain particles.
--Dave J.