Muzaffer Kal wrote:> On Fri, 02 Oct 2009 13:08:54 -0400, Jerry Avins <jya@ieee.org> wrote: > >> Muzaffer Kal wrote: >>> On Fri, 2 Oct 2009 04:55:09 -0700 (PDT), Rune Allnor >>> <allnor@tele.ntnu.no> wrote: >>>> Yes, but one does not necessarily need to recreate a physical >>>> signal from the samples. As long the data remain in digital >>>> domain, they are no more than a sequence of numbers. >>> True but to distinguish one set of numbers from another set, say to >>> make the judgment "seqeunce A has more power than sequence B" one >>> doesn't have to feed them to a DAC/scope. You can look at the >>> sequences and tell if you were to feed them to such a system they're >>> different and make qualitative judgments about them so the sequences >>> are not meaningless bunch of numbers. Under the right conditions they >>> do represent the original signals they were derived from >> Is the power your brain uses to judge the signal related to the power it >> represents? > > I am not sure how my brain works (or how well) so I can't answer that > question but what I can tell you something I know a little about. In > digital logic (say a DSP datapath) input signals with low variance > usually generate fewer transitions in the circuit so they have usually > cause lower power consumption to be processed (I added the two > usuallys because your circuit could be bound by very high leakage and > the marginal power difference because of the transistions maybe too > small to be observed or you may have a circuit which generates > internal transitions not related to its input, say to deter power > signature analysis). So it's really not true to say a sequence of > numbers are indistinguishable from others and/or they're meaningless > as long as they're numbers. > Another example is an adaptive FIR, say implementing an echo > canceller. When converged, the filter definitely knows what type of a > channel you are using and depending on how long the echo tail is or > how many taps there are on the wire causing echo, the FIR filter > consumes more or less power trying to cancel the echo. There are more > non-zero taps to be multiplied with and non-zero results to be added. > So the sequence of numbers definitely do have a consequence on the > power a digital circuit consumes to process it.True. Does that "power" represent the power of the signal in any meaningful way? How would that representation be influenced by scaling? I have the power to ignore this thread. Does that count? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Doubts in Sampling
Started by ●September 30, 2009
Reply by ●October 2, 20092009-10-02
Reply by ●October 2, 20092009-10-02
>On 2 Okt, 13:13, "Nikhil A D" <nikhil2...@gmail.com> wrote: >> >On 01-10-2009 at 01:32:50 Rune Allnor <all...@tele.ntnu.no> wrote: >> >> (...) >> I disagree. I want to distinguish between the sampled signal and the >> sequence of numbers. > >*Almost* correct, but you didn't define what a 'sampled signal' is. >Thetrem can be interpreted as either "a physical quantity that has >been fed to the input of an ADC" or "the sequence of numbers emerging >at the output of an ADC." You need to be acutely aware of the two >meanings, and the possible mix-up. > >I'll rephrase to avoid the term: You have to distinguish between > >1) the physical quantity that was sampled >2) the sequence of numbers made up by the samples. >Hey Rune, thanks a lot for defining these things. I meant exactly the same.>> A sampled signal is still a physical quantity. > >Of course the physical quantity that was sampled is >a physical quantity. To the extent it still exists after >samplig took place. Again, your term 'sampled signal' >has not been defined. > >> A >> sequence of numbers is a representation of the sampled signal, > >The discrete representation of the physical quantity that was >sampled is a sequence of numbers. > >> like a >> snapshot taken and is stored in some memory. Now to re-create thesampled>> signal (say, a voltage signal) from the sequence of numbers stored inthe>> memory requires electrical energy. > >Yes, but one does not necessarily need to recreate a physical >signal from the samples. As long the data remain in digital >domain, they are no more than a sequence of numbers. > >Rune >Yes, you are right. As long as the data remain in digital domain (ones and zeros inside a DSP's memory), they are no more than a sequence of numbers. But I am not sure about the following statement of yours: "... but one does not necessarily need to recreate a physical signal from the samples." I believe that for almost all systems that need a physical quantity as an input, there is some kind of output that can be physically perceived. Examples of such outputs are: Audio, Video. Let us take an example to see how the "digital" signal's energy is related to the physical quantity generated from it. I take a photograph of a dark room using a digital camera, without turning on camera's flash and keeping shutter open for, say, time T. Now, I take photograph of a bright Sun using the same conditions as above. I want to view these two "digital signals" on a monitor's screen. Now, the "dark" image will take lesser energy when displayed on the monitor than the "bright" image. This is because in the first place, when I sampled the two scenes using the digital camera, the energy captured in the second was obviously more, and hence, it resulted in more energy consumption when displayed on the monitor's screen. Do you agree? Nikhil
Reply by ●October 2, 20092009-10-02
>Nikhil A D wrote: >>> On 01-10-2009 at 01:32:50 Rune Allnor <allnor@tele.ntnu.no> wrote: >>> >>> (...) >>>> Once the signal has been sampled, you only have a sequence of >>>> numbers, not a physical quantity. Since no physical quantities >>>> are involved, the term 'energy' has no relevance. >>> (...) >>> >>> >>> I support this. >>> There is no energy in samples (numbers). >>> They are just information. >>> Sampled signal is an idea of real signal. >>> >>> >>> -- >>> Mikolaj >>> >> >> I disagree. I want to distinguish between the sampled signal and the >> sequence of numbers. A sampled signal is still a physical quantity. A >> sequence of numbers is a representation of the sampled signal, like a >> snapshot taken and is stored in some memory. Now to re-create thesampled>> signal (say, a voltage signal) from the sequence of numbers stored inthe>> memory requires electrical energy. >> >> It is like this.... we represent sinusoidal signal as sin (wt). To >> generate sin (wt), we need a function generator, which consumesenergy.>> Likewise, a sampled signal is represented as... for example, [1.2,2.7,>> 5.6, 4.1]. To generate a physical signal from this needs energy. > >Does the energy required to run the function generator equal the energy >of the signal being reproduced? If not, how are they related? We're back>to "Nothing is better than a piece of bread." > >Jerry >-- >Hi Jerry, Let us assume that we have an ideal function generator. An ideal function generator is the one which has zero loss on energy inside it and the energy at the output is the same as the input. With such a function generator if I reproduce 'sin(wt)' and connect a 100 Ohm resistor across the two output terminals, then the power dissipated in the resistor has to be same as the power drawn from the AC supply on which the function generator is running. Let's take about digital signals. From a digital signal representing the sequence [1.2, 2.7, 5.6, 4.1], if I create a voltage signal with the same sample values (using a dumb digital-to-analog converter that does not have an interpolator), then the energy of the voltage signal is the same as the that of discrete samples taken before converting the samples in a sequence of bits (using an ADC) and storing them in a memory. Nikhil
Reply by ●October 2, 20092009-10-02
On 2 Okt, 21:24, "Nikhil A D" <nikhil2...@gmail.com> wrote:> >On 2 Okt, 13:13, "Nikhil A D" <nikhil2...@gmail.com> wrote: > >> >On 01-10-2009 at 01:32:50 Rune Allnor <all...@tele.ntnu.no> wrote: > > >> (...) > >> I disagree. I want to distinguish between the sampled signal and the > >> sequence of numbers. > > >*Almost* correct, but you didn't define what a 'sampled signal' is. > >Thetrem can be interpreted as either "a physical quantity that has > >been fed to the input of an ADC" or "the sequence of numbers emerging > >at the output of an ADC." You need to be acutely aware of the two > >meanings, and the possible mix-up. > > >I'll rephrase to avoid the term: You have to distinguish between > > >1) the physical quantity that was sampled > >2) the sequence of numbers made up by the samples. > > Hey Rune, thanks a lot for defining these things. I meant exactly the > same. > > > > > > > > >> A sampled signal is still a physical quantity. > > >Of course the physical quantity that was sampled is > >a physical quantity. To the extent it still exists after > >samplig took place. Again, your term 'sampled signal' > >has not been defined. > > >> A > >> sequence of numbers is a representation of the sampled signal, > > >The discrete representation of the physical quantity that was > >sampled is a sequence of numbers. > > >> like a > >> snapshot taken and is stored in some memory. Now to re-create the > sampled > >> signal (say, a voltage signal) from the sequence of numbers stored in > the > >> memory requires electrical energy. > > >Yes, but one does not necessarily need to recreate a physical > >signal from the samples. As long the data remain in digital > >domain, they are no more than a sequence of numbers. > > >Rune > > Yes, you are right. As long as the data remain in digital domain (ones and > zeros inside a DSP's memory), they are no more than a sequence of numbers. > > But I am not sure about the following statement of yours: > > "... but one does not necessarily need to recreate a physical > signal from the samples." > > I believe that for almost all systems that need a physical quantity as an > input, there is some kind of output that can be physically perceived. > Examples of such outputs are: Audio, Video.> Do you agree?No. In radar and sonar the output from a measurement is a single number, the time of arrival of the echo. Sure, in a lot of applications the end product is an image or other presentation that ahuman can percieve, but in others the numerical output of the sensor is used as input to some (numerical) navigation or guidance system. Rune
Reply by ●October 2, 20092009-10-02
On Fri, 02 Oct 2009 14:23:40 -0400, Jerry Avins <jya@ieee.org> wrote:>Muzaffer Kal wrote: >> On Fri, 02 Oct 2009 13:08:54 -0400, Jerry Avins <jya@ieee.org> wrote: >> >>> Muzaffer Kal wrote: >>>> On Fri, 2 Oct 2009 04:55:09 -0700 (PDT), Rune Allnor >>>> <allnor@tele.ntnu.no> wrote: >>>>> Yes, but one does not necessarily need to recreate a physical >>>>> signal from the samples. As long the data remain in digital >>>>> domain, they are no more than a sequence of numbers. >>>> True but to distinguish one set of numbers from another set, say to >>>> make the judgment "seqeunce A has more power than sequence B" one >>>> doesn't have to feed them to a DAC/scope. You can look at the >>>> sequences and tell if you were to feed them to such a system they're >>>> different and make qualitative judgments about them so the sequences >>>> are not meaningless bunch of numbers. Under the right conditions they >>>> do represent the original signals they were derived from >>> Is the power your brain uses to judge the signal related to the power it >>> represents? >> >> I am not sure how my brain works (or how well) so I can't answer that >> question but what I can tell you something I know a little about. In >> digital logic (say a DSP datapath) input signals with low variance >> usually generate fewer transitions in the circuit so they have usually >> cause lower power consumption to be processed (I added the two >> usuallys because your circuit could be bound by very high leakage and >> the marginal power difference because of the transistions maybe too >> small to be observed or you may have a circuit which generates >> internal transitions not related to its input, say to deter power >> signature analysis). So it's really not true to say a sequence of >> numbers are indistinguishable from others and/or they're meaningless >> as long as they're numbers. >> Another example is an adaptive FIR, say implementing an echo >> canceller. When converged, the filter definitely knows what type of a >> channel you are using and depending on how long the echo tail is or >> how many taps there are on the wire causing echo, the FIR filter >> consumes more or less power trying to cancel the echo. There are more >> non-zero taps to be multiplied with and non-zero results to be added. >> So the sequence of numbers definitely do have a consequence on the >> power a digital circuit consumes to process it. > >True. Does that "power" represent the power of the signal in any >meaningful way? How would that representation be influenced by scaling?The influence of scaling on a numeric stream is no more than the influence of a 1x vs 10x probe you used in your scope. If you don't know what scaling you used or what probe you used the absolute magnitude of the numbers you observe are meaningless in either case, only the relative values are. The same way if you don't know the gain of your input amplifier in an analog path, the result is the same as not knowing the number you multiply a stream of numbers with.>I have the power to ignore this thread. Does that count?Claiming you have a certain power doesn't really mean much. The only proof of power is the ability to exercise it ;-) -- Muzaffer Kal DSPIA INC. ASIC/FPGA Design Services http://www.dspia.com
Reply by ●October 2, 20092009-10-02
Muzaffer Kal wrote: ...> The influence of scaling on a numeric stream is no more than the > influence of a 1x vs 10x probe you used in your scope. If you don't > know what scaling you used or what probe you used the absolute > magnitude of the numbers you observe are meaningless in either case, > only the relative values are. The same way if you don't know the gain > of your input amplifier in an analog path, the result is the same as > not knowing the number you multiply a stream of numbers with.Not exactly, in that the scale markings on my scope change when I change probes, so I read voltage directly with either configuration. (But that's a digression.) Do you really believe that the power to process a signal represents the power of the signal itself in any meaningful way?>> I have the power to ignore this thread. Does that count? > > Claiming you have a certain power doesn't really mean much. The only > proof of power is the ability to exercise it ;-)In this case, I have that power but I chose not to exercise it. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 2, 20092009-10-02
Nikhil A D wrote:>> On 2 Okt, 13:13, "Nikhil A D" <nikhil2...@gmail.com> wrote: >>>> On 01-10-2009 at 01:32:50 Rune Allnor <all...@tele.ntnu.no> wrote: >>> (...) >>> I disagree. I want to distinguish between the sampled signal and the >>> sequence of numbers. >> *Almost* correct, but you didn't define what a 'sampled signal' is. >> Thetrem can be interpreted as either "a physical quantity that has >> been fed to the input of an ADC" or "the sequence of numbers emerging >> at the output of an ADC." You need to be acutely aware of the two >> meanings, and the possible mix-up. >> >> I'll rephrase to avoid the term: You have to distinguish between >> >> 1) the physical quantity that was sampled >> 2) the sequence of numbers made up by the samples. >> > > Hey Rune, thanks a lot for defining these things. I meant exactly the > same. > >>> A sampled signal is still a physical quantity. >> Of course the physical quantity that was sampled is >> a physical quantity. To the extent it still exists after >> samplig took place. Again, your term 'sampled signal' >> has not been defined. >> >>> A >>> sequence of numbers is a representation of the sampled signal, >> The discrete representation of the physical quantity that was >> sampled is a sequence of numbers. >> >>> like a >>> snapshot taken and is stored in some memory. Now to re-create the > sampled >>> signal (say, a voltage signal) from the sequence of numbers stored in > the >>> memory requires electrical energy. >> Yes, but one does not necessarily need to recreate a physical >> signal from the samples. As long the data remain in digital >> domain, they are no more than a sequence of numbers. >> >> Rune >> > > Yes, you are right. As long as the data remain in digital domain (ones and > zeros inside a DSP's memory), they are no more than a sequence of numbers. > > But I am not sure about the following statement of yours: > > "... but one does not necessarily need to recreate a physical > signal from the samples." > > I believe that for almost all systems that need a physical quantity as an > input, there is some kind of output that can be physically perceived. > Examples of such outputs are: Audio, Video. > > Let us take an example to see how the "digital" signal's energy is related > to the physical quantity generated from it. > I take a photograph of a dark room using a digital camera, without turning > on camera's flash and keeping shutter open for, say, time T. > Now, I take photograph of a bright Sun using the same conditions as > above. > > I want to view these two "digital signals" on a monitor's screen. Now, the > "dark" image will take lesser energy when displayed on the monitor than the > "bright" image. This is because in the first place, when I sampled the two > scenes using the digital camera, the energy captured in the second was > obviously more, and hence, it resulted in more energy consumption when > displayed on the monitor's screen. > > Do you agree?No. Differences in exposure time and lens opening effectively scale the image. A photograph of the sun and a lamp globe can appear very much the same. The actual energies of the objects are different. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 2, 20092009-10-02
Nikhil A D wrote:>> Nikhil A D wrote: >>>> On 01-10-2009 at 01:32:50 Rune Allnor <allnor@tele.ntnu.no> wrote: >>>> >>>> (...) >>>>> Once the signal has been sampled, you only have a sequence of >>>>> numbers, not a physical quantity. Since no physical quantities >>>>> are involved, the term 'energy' has no relevance. >>>> (...) >>>> >>>> >>>> I support this. >>>> There is no energy in samples (numbers). >>>> They are just information. >>>> Sampled signal is an idea of real signal. >>>> >>>> >>>> -- >>>> Mikolaj >>>> >>> I disagree. I want to distinguish between the sampled signal and the >>> sequence of numbers. A sampled signal is still a physical quantity. A >>> sequence of numbers is a representation of the sampled signal, like a >>> snapshot taken and is stored in some memory. Now to re-create the > sampled >>> signal (say, a voltage signal) from the sequence of numbers stored in > the >>> memory requires electrical energy. >>> >>> It is like this.... we represent sinusoidal signal as sin (wt). To >>> generate sin (wt), we need a function generator, which consumes > energy. >>> Likewise, a sampled signal is represented as... for example, [1.2, > 2.7, >>> 5.6, 4.1]. To generate a physical signal from this needs energy. >> Does the energy required to run the function generator equal the energy >> of the signal being reproduced? If not, how are they related? We're back > >> to "Nothing is better than a piece of bread." >> >> Jerry >> -- >> > > Hi Jerry, > > Let us assume that we have an ideal function generator. An ideal function > generator is the one which has zero loss on energy inside it and the energy > at the output is the same as the input. > > With such a function generator if I reproduce 'sin(wt)' and connect a 100 > Ohm resistor across the two output terminals, then the power dissipated in > the resistor has to be same as the power drawn from the AC supply on which > the function generator is running. > > Let's take about digital signals. > > From a digital signal representing the sequence [1.2, 2.7, 5.6, 4.1], if I > create a voltage signal with the same sample values (using a dumb > digital-to-analog converter that does not have an interpolator), then the > energy of the voltage signal is the same as the that of discrete samples > taken before converting the samples in a sequence of bits (using an ADC) > and storing them in a memory.How does that relate to the energy of the sampled signal? My pocket radio's battery is nominally 9 volts. My old car battery was 6.3 volts. Which do you suppose was more powerful? jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 3, 20092009-10-03
>> (...) >> Let us take an example to see how the "digital" signal's energy isrelated>> to the physical quantity generated from it. >> I take a photograph of a dark room using a digital camera, withoutturning>> on camera's flash and keeping shutter open for, say, time T. >> Now, I take photograph of a bright Sun using the same conditions as >> above. >> >> I want to view these two "digital signals" on a monitor's screen. Now,the>> "dark" image will take lesser energy when displayed on the monitor thanthe>> "bright" image. This is because in the first place, when I sampled thetwo>> scenes using the digital camera, the energy captured in the second was >> obviously more, and hence, it resulted in more energy consumption when >> displayed on the monitor's screen. >> >> Do you agree? > >No. Differences in exposure time and lens opening effectively scale the >image. A photograph of the sun and a lamp globe can appear very much the>same. The actual energies of the objects are different. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >As I said earlier in the my message above, both the photographs are taken under the same conditions - equal exposure time and lens opening. Nikhil
Reply by ●October 3, 20092009-10-03
>> (...) >> Let us assume that we have an ideal function generator. An idealfunction>> generator is the one which has zero loss on energy inside it and theenergy>> at the output is the same as the input. >> >> With such a function generator if I reproduce 'sin(wt)' and connect a100>> Ohm resistor across the two output terminals, then the power dissipatedin>> the resistor has to be same as the power drawn from the AC supply onwhich>> the function generator is running. >> >> Let's take about digital signals. >> >> From a digital signal representing the sequence [1.2, 2.7, 5.6, 4.1],if I>> create a voltage signal with the same sample values (using a dumb >> digital-to-analog converter that does not have an interpolator), thenthe>> energy of the voltage signal is the same as the that of discretesamples>> taken before converting the samples in a sequence of bits (using anADC)>> and storing them in a memory. > >How does that relate to the energy of the sampled signal? My pocket >radio's battery is nominally 9 volts. My old car battery was 6.3 volts. >Which do you suppose was more powerful? > >jerry >-- >Engineering is the art of making what you want from things you can get. >If the exact definition of energy or power is not available, we talk about normalized energy or normalized power. Normalized power is the power dissipated in a 1 ohm resistor. So at the output of DAC if we have samples [1.2, 2.7, 5.6, 4.1], then their (normalized) energy is (1.2)^2 + (2.7)^2 + (5.6)^2 + (4.1)^2 = 56.9 . In the case of your batteries, 9 volts and 6 volts, which one is more powerful will depend on the actual current ratings on the batteries. But if we accept the definition of normalized power, then 9 volt battery is more powerful. Nikhil
