'

Fellow Travelers:

'

The original question would be hilarious  if it were merely a joke,

or perhaps an attempt to shake the tree to see what may fall out; 

but since it appears to be a serious one, it demands a serious

response. Think of this response as Part One of a Series.... (I'm

serious).

---------------------------

Hugh thinks "it has a lot to do with 'intellectual inertia'.".  As one

of those "burdened" by over 60 years of analog inertia, I should

not be expected to propose this test, as I often have in lectures:

'

IF ANY SIGNAL PROCESSING FUNCTION IS REALIZABLE

IN THE DIGITAL DOMAIN - WITHOUT SIGNIFICANT LOSS

OF NECESSARY INFORMATION; OR WITHOUT CAUSING

THE INTRODUCTION OF SPURIOUS INFORMATION; AND

IT IS WITHIN THE SCOPE OF A DIGITAL METHOD USING

A READILY-AVAILABLE TECHNOLOGY; AND OPERATES

AT APPRECIABLY LOWER POWER LEVELS THAN SOME

PRIOR ANALOG METHOD; AND AT LOWER (OR EQUAL)

PRODUCT COST; THEN IT OUGHT TO BE IMPLEMENTED

IN THE DIGITAL DOMAIN.

'

That's a long expansion of what I will usually advise, which

is something like: "If you can do it digitally, then you should".

.

The problem here is that only a certain fraction of challenges 

can pass this litmus test. A vast number of signal processing

functions can only be implemented using analog techniques,

or which for numerous inherent reasons are better performed 

in the analog domain. This is clearly true for microwave radio

systems (I hold up an i-phone and declare; "This is the most

advanced example of an almost-all analog system") but also

for such common things as your car's fuel-injection system, its

front-, rear- and side-looking radar systems (at about 77GHz),

its (several) air-bag accelerometers and analog interfaces, as

well as several dozen analog sensors scattered around the

car but out of sight.

'

It would be easy to cite many more examples of the necessity

of analog circuits, in industry, medicine, avionics. and defense

systems.  One example - one that is of universal importance -

is the humble power supply (not exactly signal processing, but

deeply and necessarily an analog function).

'

ANALOG PROCESSING IS CLOSE TO NATURE. ONE CAN

FIND ENDLESS EXAMPLES IN EVERY PLANT AND TREE;

EVERY MOVING CREATURE IS LADEN WITH THE MOST

BEAUTIFUL, EXOTIC -  AND STILL MOSTLY MYSTERIOUS

- ANALOG SIGNAL PROCESSING.  MAMMALIAN BRAINS 

EMPLOY A NEAR-ASTRONOMICAL NUMBER OF ANALOG

SIGNAL PATHS OPERATING ON BILLIONS OF NEURONS,

ANALOG ELECTRICAL ELEMENTS EACH OF WHICH CAN

BE VIEWED (SIMPLISTICALLY, BUT CORRECTLY) AS AN

INTEGRATOR OF ELECTRICAL CHARGE, AUGMENTED BY

A CLUSTER OF DECISION ELEMENTS, WHILE INVOKING

FEEDBACK - A GOOD OLD ANALOG RECIPE.

.

This is an observable fact. Now, who would like to stand up

and offer to perform the function of a human brain entirely in

some sort of digital domain: and get it all in the same space;

and run it from a few watts of power? And have it produced

by totally unskilled labour, with very high yields?

.

One final example of ANALOG POWER is a common device

that can accept as its input signal a wide range of frequencies,

perform an FFT on this input within less than one nanosecond,

and deliver this transform at its output, using zero power, and

weighing about one gram?

.

What am I talking about?

'

Barrie

Hi Jesús, for some applications it is still more natural to work in the continuous domain. To give you an example: I am currently working on a time warp problem. The optimal time warp is to be estimated, and this can be considered to be a continuous function. Although the original signals are discrete, the discretization is treated as noise and for this particular problem the maths become simpler in continuous form (and they avoid a nasty non-uniform resampling process).

I think it has a lot to do with "intellectual inertia". Older electrical/electronic engineers (who wrote most of the classic books in this area) grew up playing with (analogue) electronics kits from Radioshack (or Dick Smith here in Australia). Then something miraculous happened in the late 70s and early 80s! Younger engineers were lucky enough to start seeing (digital) computers in their homes to play with and program when they were growing up. This of course changes the whole way you think and see the world (as an engineer).

At a control conference I was at recently (MSC2015), it was clear that the majority of people still prefer to design controllers using continuous-time techniques. They then discretize them immediately prior to implementation. I think aesthetics plays a part here. I hear people say that differential equations have a certain beauty that cannot be found in discrete time; but for me, the awesome efficiency of a finite difference equation just blows my mind. Of course in control systems, we need to remember that the real-world (that we are trying to control) does operate in continuous time and that it is only our controller that is discrete.

The main (only?) reason why I would want to implement an analogue controller (or filter) is if I wanted to make a passive circuit for only a few bucks, without the use of a computer (with A2D, D2A, etc). But this is now becoming harder to justify as simple processing boards just keep on getting cheaper and easier to program!  

Hi,

in an audio quality domain continuos (analogue) time signal processing could be preferred, for example in sound quality testing or for music performance.

The frequent use of difference equations led us to forget the differential equations but there are situations where difference equations are difficult to obtain or have infinite order. It is the case of fractional differential equations. Happily we have  discrete-time differential equations that allow to establish a bridge between continuous-time and discrete-time. You may argue, as I heard before, that the fractional differential equations do not have any special interest in applications. It is not true. Our world is mainly fractional. There are many applications and fractional control is becoming standard. On the other hand the processing on time scales led to a unified formulation and allow the study o mixed continuous-discrete systems.

'

Fellow Travelers:

'

The original question would be hilarious  if it were merely a joke,

or perhaps an attempt to shake the tree to see what may fall out; 

but since it appears to be a serious one, it demands a serious

response. Think of this response as Part One of a Series.... (I'm

serious).

---------------------------

Hugh thinks "it has a lot to do with 'intellectual inertia'.".  As one

of those "burdened" by over 60 years of analog inertia, I should

not be expected to propose this test, as I often have in lectures:

'

IF ANY SIGNAL PROCESSING FUNCTION IS REALIZABLE

IN THE DIGITAL DOMAIN - WITHOUT SIGNIFICANT LOSS

OF NECESSARY INFORMATION; OR WITHOUT CAUSING

THE INTRODUCTION OF SPURIOUS INFORMATION; AND

IT IS WITHIN THE SCOPE OF A DIGITAL METHOD USING

A READILY-AVAILABLE TECHNOLOGY; AND OPERATES

AT APPRECIABLY LOWER POWER LEVELS THAN SOME

PRIOR ANALOG METHOD; AND AT LOWER (OR EQUAL)

PRODUCT COST; THEN IT OUGHT TO BE IMPLEMENTED

IN THE DIGITAL DOMAIN.

'

That's a long expansion of what I will usually advise, which

is something like: "If you can do it digitally, then you should".

.

The problem here is that only a certain fraction of challenges 

can pass this litmus test. A vast number of signal processing

functions can only be implemented using analog techniques,

or which for numerous inherent reasons are better performed 

in the analog domain. This is clearly true for microwave radio

systems (I hold up an i-phone and declare; "This is the most

advanced example of an almost-all analog system") but also

for such common things as your car's fuel-injection system, its

front-, rear- and side-looking radar systems (at about 77GHz),

its (several) air-bag accelerometers and analog interfaces, as

well as several dozen analog sensors scattered around the

car but out of sight.

'

It would be easy to cite many more examples of the necessity

of analog circuits, in industry, medicine, avionics. and defense

systems.  One example - one that is of universal importance -

is the humble power supply (not exactly signal processing, but

deeply and necessarily an analog function).

'

ANALOG PROCESSING IS CLOSE TO NATURE. ONE CAN

FIND ENDLESS EXAMPLES IN EVERY PLANT AND TREE;

EVERY MOVING CREATURE IS LADEN WITH THE MOST

BEAUTIFUL, EXOTIC -  AND STILL MOSTLY MYSTERIOUS

- ANALOG SIGNAL PROCESSING.  MAMMALIAN BRAINS 

EMPLOY A NEAR-ASTRONOMICAL NUMBER OF ANALOG

SIGNAL PATHS OPERATING ON BILLIONS OF NEURONS,

ANALOG ELECTRICAL ELEMENTS EACH OF WHICH CAN

BE VIEWED (SIMPLISTICALLY, BUT CORRECTLY) AS AN

INTEGRATOR OF ELECTRICAL CHARGE, AUGMENTED BY

A CLUSTER OF DECISION ELEMENTS, WHILE INVOKING

FEEDBACK - A GOOD OLD ANALOG RECIPE.

.

This is an observable fact. Now, who would like to stand up

and offer to perform the function of a human brain entirely in

some sort of digital domain: and get it all in the same space;

and run it from a few watts of power? And have it produced

by totally unskilled labour, with very high yields?

.

One final example of ANALOG POWER is a common device

that can accept as its input signal a wide range of frequencies,

perform an FFT on this input within less than one nanosecond,

and deliver this transform at its output, using zero power, and

weighing about one gram?

.

What am I talking about?

'

Barrie

@BarrieGilbert: Sounds like the inner ear, or perhaps only the cochlea?

That was an inspiring response btw. I'll be waiting for part 2.

.

Steven:

.

Good! An excellent guess, but not the one I had in mind.

(Note the Condition:  "within less than one nanosecond".

And although the cochlea operates in the "ultra-green"

zone, there is a small fuel (ATP) burden in making this

marvellous engine run.)

.

Just for the fun of it, I'll keep the challenge dangling for

at least another nanosecond.

.

Barrie

@BarrieGilbert:A detailed answer and excellent explanation. Really appreciated. But what about the processing in digital domain.

@BarrieGilbert: My second guess: a tiny prism. Some cameras use trichroic prisms, although I believe that the individual prisms weigh far less than 1g there.

Thank you all for your responses.

@BarrieGilbert: Actually It was a serious question but also a bit provocative because I wanted to generate some reaction.

For those of us who always do discrete-time processing, It is not difficult to forget the usefulness continuous-time. So I wanted some examples to have in mind. And you have given me some of them.

By the way, @BarrieGilbert, regarding your challenge I would say an optical aperture (similar to Steven's answer but simpler), if you light it up, you will see in far-field the Fourier transform of the aperture (due to Fraunhofer diffraction). But for that to be true the light should be monocromatic, which I think that cannot be considered "wide range of frequencies".

@BarrieGilbert: I have already introduced all that in my lectures! It was a pleasure to read your nature inspired, correct and naturally beautiful and inspiring comment.  

.

Jesus:

.

Yes, Optics is certainly the domain. The

element I have in mind is a simple prism. 

.

Barrie

Yes, Information with help of technology development and proper utilization of domains easily we can understand any technology and domains .

Hello. Many signal processing techniques were developed using continuous time mathematics. You need to separate the theoretical basis for estimation theory and signal processing from its practical implementation. Many of the results on measure theory, convergence of Fourier transforms, convergence of the Kalam Bucy filter were done for continuous time systems and these insights were used to develop the theory, where possible, for discrete time systems. It would be a big mistake to think that just because we don't, at least at the moment, implement signal processing algorithms in continuous time that we don't need the theory! Many areas in engineering and science would simply not exist if the theory for continuous time systems had not been developed. Think about ODEs, PDEs, stochastic processes, etc. The discrete-time systems approaches to many of these are just a bolt-on to the theory via discretised approximation.

BTW I think there are some continuous-time processing techniques, like DNA computing, that use the properties of natural systems to solve complex problems.

Graham

I agree with a lot of things you wrote, but we do not need any continuous background to develop discrete-time ODE, PDE, stochastic processes, transforms ... We can do everything from a discrete-time framework and without any approximation. It's not correct to assume that discrete means approximation to continuous. There are signals and systems that are intrinsically continuous, while others similarly are discrete. Sometimes you can go from continuous to discrete and vice-versa without loosing or inserting new information. Other times, no.

I love the interest aroused by this question.

Thank you all for the debate and the interesting contributions.

I agree with Manuel that a lot of theory is directly developed for discrete-time processes but I also see Graham's point: Continuous time framework is somewhat easier in most cases and after solving that you can have intuitions for solving related Discrete time cases (without having to rely in any approximation).

.

Fellow Travelers:

The previous two comments assert that

(1) It’s not correct to assume that discrete means approximation to continuous.

(2) One can implement CT-CA functions without relying on any approximation.

.

I believe this basic point needs to be worded more carefully,

since it is manifestly apparent that the very word “discrete”

fundamentally implies the use of discrete steps of a CT-CA

signal in both time and amplitude, losung something in the

crucial process of analogbinary conversion.

.

The point to be made is that the numerous signal-processing

methodologies developed during the early days of electronics

can be adapted for implementation in DT-DA systems without

sacrificing the PRACTICAL accuracy of the function - WITHIN

a SPECIFIC APPLICATION,  inherently limited in bandwidth,

linearity and noise performance.

.

In this regard, DT-DA systems often provide better practical

accuracy than prior analog systems, always  prone to many

sorts of limitations and errors [”approximations”] arising from

the absolute [“tolerance”] and relative [“matching”] variances

in the circuit components, the inherent nonlinearity, noise

and bandwidth limitations of the active elements, and a

variety of other sources of practical processing “errors”.                                    

.

It is only the progressive advances that have been made

in analog-optimized technologies that have minimized all

of the above errors to amazingly low levels, and – most

importantly – have allowed the fabrication of extremely

accurate analogbinary gateways having the advanced

performance required to make digital signal processing

even possible in the first place.

.

This is NOT an  either-or  matter as the original question

suggests.  Ontara is a Sanskrit word meaning “taking the

next step in balance” -  the idea that a bold new journey

should be undertaken only after fully assessing ALL the

relevant circumstances.

.

Every new day is the right time to practice Ontara.

.

Barrie