Frequency Domain and Time Domain relationships

[Tinkerer]

From many posts across the forum, I can see that many people would appreciate an explanation of frequency domain and time domain and how these domains apply to the PULSE INDUCTION METAL DETECTORS.

I think that a thorough discussion about this subject would be welcome by many, so please ask relevant questions.

And please post explanations, those who have the knowledge on the subject.

I will try to give it a start:

In general, PI detectors are considered as Time Domain detectors. However, there are many frequency domain aspects involved too.
There is the frequency of the pulse repetition rate, Pulses Per Second. PPS
This has much influence on the integrating time of the target signal.
Integrating many pulses produces a good Signal to Noise Ratio. S/N

This in turn has much influence on the sweep speed. Meters per second and response time.

So let's talk a bit about this and then add another frequency involved.

Tinkerer

[hobbes_lives]

IMHO, the DSP guide offers a wealth of information on processing in both domains, and is available for online reading...

http://www.dspguide.com/

[mikebg]

Tinkerer, you started to become a Thinker.
Please read Patent US 4,506,225.

[Tinkerer]

IMHO, the DSP guide offers a wealth of information on processing in both domains, and is available for online reading...

http://www.dspguide.com/

hobbes,

thanks for the feedback and the information. I downloaded the full zip file here:

http://www.analog.com/static/importe...k_dspguide.zip

but honestly, I have little hope to be capable of ever fully mastering DSP.

I can only hope that, "with a little help from my friends" from the forum, I will get to understand the most basic principles.

Tinkerer

[Tinkerer]

Tinkerer, you started to become a Thinker.
Please read Patent US 4,506,225.

mikebg,

thanks for the link to the patent.
Yes, indeed, this is the same technique that I am using. Looking at the date of the patent, we know that today we have many splendid tools and components that were not available at that time.

This includes DSP.

So, maybe you will be so kind as to help me understanding how the various time domains and frequency domains of my detector interact. Only if I fully understand the interactions, can I suggest a way to extract the target information by using DSP.

In my post above, I mentioned different frequencies. There are many more different frequencies involved.
When I extract synchronous samples, I pick specific times along the cycle.
I chose these specific times because I have noted that certain target characteristics like the TC of the target and magnetic response show up, by changing the signal wave form, at these times.

I have also noticed that the TC of the coil, the duration of the TX pulse and the TC of the target have a relationship that changes every factor if just one factor is changed.

There are so many factors inter related with the TEM PI and I need to know and understand all these relationships. Once these relationships are deciphered, the design will become very easy.

So my questions are so many, I don't even know what to ask first. for example: the TC of the coil, I think it can be considered to belong into the frequency domain. To get the best magnetic response from a FE target, the sample must be taken at about 1TC of the coil. A perfectly linear ramp would be best. The timing of the FE sample belongs into the time domain.

Obviously I need help. Please!!

Tinkerer

[mikebg]

NARROW BAND AND WIDE BAND METAL DETECTORS

TOOLS FOR ANALYSIS AND SYNTHESIS

There is a silly claim that
there are metal detectors operating in the FD (frequency domain).

This is nonsense, because everything in our real world happens in time. Even my oscilloscope connected to my VLF metal detector shows that it operates in TD (time domain). (My scope measures the period T of periodic functions and shows it as frequency f=1/T).

The FD was created almost 200 years ago as powerful tool for analysis and syntesis (design not only of all types metal detectors :-). Instead the variable t (time), the FD uses as reference T (period of a periodic function), but the variable is periods (cycles) pro second f=1/T.

The advantage of FD is because a complicated math operation "convolution" used in TD, the FD uses a more simple operation "multiplication" and even "summation" if all values are expressed in dB (decibels).

According to the FD, there are only two types metal detectors NB (narrow band) and WB (wide band).

To demonstrate different tools for analysis and synthesis (design), I will use a device with input and output as an amplifier. Below is illustrated how to calculate the output in real world, in FD and in TD. All know that the amplifier has an own parameter named "gain". However the gain depends on frequency.

Oops! I started to speak in frequency domain.

In real world, the output is calculated with solving differential equation (only MADLAB participants use this :-).
In FD it is calculated with multiplication of frequency spectrums.
In TD it is calculated with complicated math operation "convolution".

[Ferric Toes]

Although I have been involved with PI metal detectors since 1966, which is accepted as a time domain principle, immediately prior to that I was involved for 2.5 years in airborne radar development. Yet again, prior to even that, did 2.5 years on transistorised TV tuner design. Always been interested in shortwave and vhf communications and even at this moment have a R1155A and two R1132A WW2 RAF receivers that I am restoring to operating condition. Point is that I am familiar with both TD and FD terminology and also probably guilty of using inappropriate terms at times. Basically I regard TD as being measurement of a return signal at some time after the cessation of the transmitted or exciting signal. Radar is TD if you like as you are looking for reflected signals in between bursts of FD (35GHz in the case of the radar I was involved with). I can't remember what the pulse repetition frequency (prf) was but it must have been many tens of kHz, and multiplexed side to side, for a plane flying at Mach 1 at low level. So here also we have an apparent mixing of terms.

I notice that Yves Lamontagne in his doctorate thesis describes continuous triangular wave TX and RX processing as TD, although there is no off time. Here it is the RX processing (sampling) that takes place after successive time gates following each transition of the TX wave.

One term that I have seen used many times is "demodulator" as referring to the operation of the sample gates. To my way of thinking, this is wrong, as you are not retrieving a signal from a modulated carrier wave in the accepted radio sense.

Eric.

[Tinkerer]

TEM and UTEM

Lamontagne link:

http://geophysics.kos.net/website/pd...0Advantage.pdf

[Carl-NC]

Mike, you are correct that metal detectors are all time-domain in how the signal is processed. There is a little looseness in terminology when it comes to TD vs FD, mostly for marketing (layman) reasons. Eric is right that we usually consider off-time sampling to be TD while continuous sampling is FD, but as I said in the Triangle thread the difference between TD and CW sampling is splitting hairs. There is another aspect, in that CW detectors (so-called FD) result in an RX signal that is both amplitude and phase modulated, while TD is amplitude and time modulated. But time and phase are still dealt with in almost the same exact way.

Eric, I still consider samplers to be demodulators... the TX signal isn't modulated but the RX signal is.

[Qiaozhi]

One term that I have seen used many times is "demodulator" as referring to the operation of the sample gates. To my way of thinking, this is wrong, as you are not retrieving a signal from a modulated carrier wave in the accepted radio sense.

Eric.

If you consider a metal target as modulating the TX signal, then a sample gate can be called a demodulator. The sampling gate and associated filters effectively remove the carrier signal (the TX) leaving the baseband signal (the target).

[Ferric Toes]

If you consider a metal target as modulating the TX signal, then a sample gate can be called a demodulator. The sampling gate and associated filters effectively remove the carrier signal (the TX) leaving the baseband signal (the target).

Hi Qiaozhi and Carl,

Not worth arguing about, but with traditional PI the TX is well and truly off when sampling takes place, particularly at medium and late times. The only time I would consider that the return signal is modulating the TX is if the TX is still ringing.

Eric.

[mikebg]

FD as design tool

Attached below image illustrates how is obtained information for design of a BPF (band pass filter) which is connected after demodulator to suppress noise and GNDds (demodulated ground signal).

When operator swings search head, he can not keep equal distance to ground and GND signal appears modulated. Since synchronous demodulator is not ideal balaanced, it sees some modulation and generates GNDds as a pulse which width is almost as time of a swing.

If there is a relatively small target, search head passes quick over it. The demodulator generates TGTds (demodulated target signal) as a short pulse which duration is small relatively to time of a coil swing.
To design BPF, we should transform both pulses in FD. We will see that they differs in frequency spectrum. For example the spectrum of GNDds has maximal frequency 4Hz and large DC component, but the TGTds spectrum contains frequencies untill 16 Hz and has maximum at 8Hz as is illustrated on the right side diagram.
Remains to design a BPF to suppress frequencies below 4 Hz and above 16Hz.
Let a "MadLabs Inc."(c)(tm)(r) participant explain how will solve this problem using only Time domain.

[Davor]

I would consider that the return signal is modulating the TX is if the TX is still ringing.

I'd say that there is a Tx decay present because of Tx tau, but quite short. It only spoils the early samples.

[Davor]

Let a "MadLabs Inc."(c)(tm)(r) participant explain how will solve this problem using only Time domain.

Easy, a FIR filter. Much better than analogue IIR solution. However, there is a bit more to the 8kHz peak than meets the eye ... 1/f noise. Besides, the rising slope would ideally work as differentiator with nice time domain response, while the vast majority of nowadays detectors fail there.

[deemon]

As I think , we can say about FD detector if either it transmits sinusoid wave or it receives only the fundamental frequency of transmitted wave . If our device transmits 2 or 3 sinusoid waves - it still remains in the frequency domain . In other cases it's a TD device , IMHO .