What is the relationship between tuning rate and bandwidth in receiver design?

[Firefox123]

On page 109 of David Adamy's book EW 101: A First Course in Electronic Warfare there is the following comment:

In general, the tuning rate of the searching receiver (the amount of frequency spectrum searched per unit of time) must be no greater than one bandwidth in a time equal to the inverse of the bandwidth. For example, if the searching receiver has a 1-MHZ bandwidth, it can sweep no faster than 1MHz per microsecond.

I'm not sure exactly why the tuning rate "must" not exceed this value...can anyone clear this up for me?

Maybe this is something really simple and I am just missing it...

 

[sophiecentaur]

It means that you can't 'sweep' at a higher rate than this. If the bandwidth of the receiver is too narrow for the sweep rate, the receiver will not have time to establish whether or not there's a signal there. The bandwidth limits the rate of response.

 

[Firefox123]

Thanks for the reply.

It means that you can't 'sweep' at a higher rate than this.

Correct...this is exactly what Adamy is saying...

If the bandwidth of the receiver is too narrow for the sweep rate, the receiver will not have time to establish whether or not there's a signal there. The bandwidth limits the rate of response.

Sure...it makes sense that there would be a maximum sweep rate for some given bandwidth...the hardware/firmware has a limit on what it can process...

But...why is this maximum rate necessairly the inverse of the bandwidth?

I would think the maximum rate would be hardware specific, not a general rule...

What am I missing about the rate being the inverse of the bandwidth of the receiver?

 

[sophiecentaur]

You are right in that this rule is a bit arbitrary. The actual sweep limit depends upon a number of things. For instance, it will depend on the actual receiver filter characteristic and the modulation method - and the content of the transmission at the time the receiver happens to be sweeping past. If SSB, which has no carrier, is used and the receiver tunes through during a pause in speech, it will be missed completely.
However, the time taken for the receiver to register the presence of a signal will be 'related' to the bandwidth. It is a rule of thumb and refers to conventional transmissions and not, for example, to spread spectrum , which is deliberately spread out to avoid detection and / or to reduce interference in or outgoing.
It would be pretty much totally correct if a single carrier were to be detected in a spectrum consisting of other single carriers.

 

[waht]

Think of a high speed camera taking pictures every microsecond. If a light is flickering in milli-seconds, then it will be captured easily by the camera. If there is another light flickering at 1 nano-second, then there is no way to accurately capture it because it is faster paced light than the equipment trying to capture it.In reality there is many other factors, such as the characteristic of the resolution bandwidth filter, its rise time, swept modulation of the local oscillator, limit how fast you can sweep. If I remember correctly there is a log relationship between the bandwidth and sweep time.

 

[Firefox123]

You are right in that this rule is a bit arbitrary. The actual sweep limit depends upon a number of things. For instance, it will depend on the actual receiver filter characteristic and the modulation method - and the content of the transmission at the time the receiver happens to be sweeping past.

Agreed...

If SSB, which has no carrier, is used and the receiver tunes through during a pause in speech, it will be missed completely.

Yep...that does happen with SSB transmissions...

However, the time taken for the receiver to register the presence of a signal will be 'related' to the bandwidth. It is a rule of thumb and refers to conventional transmissions and not, for example, to spread spectrum , which is deliberately spread out to avoid detection and / or to reduce interference in or outgoing.
It would be pretty much totally correct if a single carrier were to be detected in a spectrum consisting of other single carriers.

I think Adamy is really talking in the context of detecting either radar pulses or communications signals (although I assume he is leaving out any DSSS or FHSS signals)...

I will think on this more...

 

[Firefox123]

Think of a high speed camera taking pictures every microsecond. If a light is flickering in milli-seconds, then it will be captured easily by the camera. If there is another light flickering at 1 nano-second, then there is no way to accurately capture it because it is faster paced light than the equipment trying to capture it.

That is a good example...especially for people who are not engineers...

In reality there is many other factors, such as the characteristic of the resolution bandwidth filter, its rise time, swept modulation of the local oscillator, limit how fast you can sweep. If I remember correctly there is a log relationship between the bandwidth and sweep time.

It's been a long time since I've looked at the equations for sweep time...time to take another look I see...

I'm still not completely understanding this as an "upper limit"...I need to think about this more...it is likely I am over complicating it as I often do...

Thanks for the replies...I will likely have more comments/questions within the next few days...

 

[sophiecentaur]

Think of a high speed camera taking pictures every microsecond. If a light is flickering in milli-seconds, then it will be captured easily by the camera. If there is another light flickering at 1 nano-second, then there is no way to accurately capture it because it is faster paced light than the equipment trying to capture it.

I think the effect you are describing here is the effect of sub-sampling, rather than that of a swept filter.

 

[skeptic2]

A number of years ago I was working with a spectrum analyzer and became aware that it was exceeding this limit and began wondering how it was doing it. My first thought was that it was using the cos^2Θ + sin^2Θ of the signal to develop the amplitude. That amplitude was attenuated due to the response time of the bandwidth filter. However if the response characteristic of the filter is accurately known, the amplitude can be divided by the response characteristic to get the true amplitude.

 

[sophiecentaur]

Absolutely.
In the end, you are relying on the signal to noise ratio which determines whether or not you can really tell a station is there. Higher signal means you could scan faster.
In your case, if you divide by the response of the filter, you will eventually end up multiplying the noise preferentially- not the signal.
This topic is similar to the application of the Rayleigh criterion which is used to decide whether you can resolve two stars with a given diameter of telescope. That says you can resolve them if the dip in brightness between them drops to half energy. It's arbitrary, in fact, because you can do much better with appropriate analysis (spatial filtering etc).

 

[Firefox123]

Absolutely.
In the end, you are relying on the signal to noise ratio which determines whether or not you can really tell a station is there. Higher signal means you could scan faster.
In your case, if you divide by the response of the filter, you will eventually end up multiplying the noise preferentially- not the signal.
This topic is similar to the application of the Rayleigh criterion which is used to decide whether you can resolve two stars with a given diameter of telescope. That says you can resolve them if the dip in brightness between them drops to half energy. It's arbitrary, in fact, because you can do much better with appropriate analysis (spatial filtering etc).

I've read about the Rayleigh criterion before...looks like it's time for a review of that as well...

Someone also pointed out to me the "Gabor Uncertainty Principle"...
http://www.cs.utk.edu/~mclennan/papers/FCMC-tr/node34.html

Fascinating stuff...I did not know there was something like that for frequnecy measurements, but I guess it should come as no surprise since it is a measurement after all.

 

[sophiecentaur]

I think the word is Convolution! It works in time domain, frequency domain and spatial domain and the sums are the same.

 

[Firefox123]

I think the word is Convolution! It works in time domain, frequency domain and spatial domain and the sums are the same.

What about convolution? Are you saying it is not realted to the Gabor Uncertainty Principle?

I'm familiar with convolution (not that I do it daily or anything)...perhaps I missed the point you were making...

Could you clairfy?

 

[sophiecentaur]

I'm just saying that what comes out of the filter is, I think, the result of convolving the wanted signal with the filter characteristic. It's just a matter of how much signal and how much noise gets through and then doing sums, appropriate to the modulation system and the noise characteristic. But that's the hard part. I was being unforgivably glib, I think.

 

[Firefox123]

I'm just saying that what comes out of the filter is, I think, the result of convolving the wanted signal with the filter characteristic. It's just a matter of how much signal and how much noise gets through and then doing sums, appropriate to the modulation system and the noise characteristic. But that's the hard part. I was being unforgivably glib, I think.

Sounds right to me...the output of a filter is just the input signal convolved with the impulse response of the filter...

Im assuming the filter has a linear response here...

So as far as what comes out of the filter, I agree...

But I think the "maximum" theoretical rate you can sweep something might be more fundamental than just looking at the specific receiver...I think it is related to measurement error and that Gabor Uncertainity Principle...