Nikhil A D wrote:>>> (...) >>> 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. >> > > As I said earlier in the my message above, both the photographs are taken > under the same conditions - equal exposure time and lens opening.Then either the dark image is all black or the one of the sun burned out the sensor. Do you know that a bowl of snow in good indoor lighting reflects less light than a piece of coal in sunlight? Does a negative of a bright scene have negative energy? 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 3, 20092009-10-03
Reply by ●October 3, 20092009-10-03
Nikhil A D wrote:>>> (...) >>> 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. >> > > 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.Try to crank a car with it! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 3, 20092009-10-03
On 1 ���, 02:27, "macsdev" <macs...@gmail.com> wrote:> Hi, > > I have a doubt in Sampling of Signals from a Theoretical Point of View. > When we sample a signal, are we losing anything in terms of Energy of the > signal? Intuitively, it seems so. But I also know that there is no loss of > Information (since the spectrum is still intact, if we sample at a proper > rate). Is my reasoning correct or is it flawed somewhere?Hi Macsdev. From "Theoretical Point of View" there are no energy and information losses. See the original Shannon paper about sampling (Kotelnikov work is not so obvious in this point). Shannon did only one - he represented the signal spectrum as Fourier series (FS). And he proved that FS coefficients are proportional to time samples of signal (with some sampling period) if its spectrum is bandlimited by some frequency. In original Shannon paper about sampling there is no interpolation formula for reconstruction the signal from samples. This formula is in Kotelnikov paper. And it is again the FS. In this case FS is by the sinc functions (sinc is sin(x)/x). So, if we want know anything about relationship of signal energy and its samples energy, we must see FS theory. And we see the Parseval equality - the energy of signal is equal to energy of its FS coefficients, so it is proportional to energy of its samples. Andrew.
Reply by ●October 3, 20092009-10-03
On 1 ���, 03:32, Rune Allnor <all...@tele.ntnu.no> wrote:> On 1 Okt, 00:27, "macsdev" <macs...@gmail.com> wrote: > > > Hi, > > > I have a doubt in Sampling of Signals from a Theoretical Point of View. > > When we sample a signal, are we losing anything in terms of Energy of the > > signal? Intuitively, it seems so. But I also know that there is no loss of > > Information (since the spectrum is still intact, if we sample at a proper > > rate). Is my reasoning correct or is it flawed somewhere? > > Flamebait? OK, here we go: > > 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. > > RuneHi Rune. Macsdev is first speaking about "Theoretical Point of View", so there are no numbers, there are only x(kdt) - samples with absolute precision and with concrete dimension. So "physical quantities" of samples energy has relevance. Andrew.
Reply by ●October 3, 20092009-10-03
On 2 ���, 10:49, "Nikhil A D" <nikhil2...@gmail.com> wrote:> An ideal band-limited signal, which has infinite duration, has infinite > energy. > Nikhil >Hi Nikhil. "An ideal band-limited signal, which has infinite duration, has infinite energy." There is not true. Let as x(t) = sinc(x), sinc(x) = sin(x)/x, x= 2piF0t. x(t) is bandlimited by 2F0 (complex FT), x(t) has infinite duration in time, x(t) has limited energy - the energy of x(t) = 1/(2F0). Andrew.
Reply by ●October 3, 20092009-10-03
"Jerry Avins" <jya@ieee.org> wrote in message news:ZeIxm.15008$ma7.12687@newsfe04.iad...> Nikhil A D wrote: >>>> (...) >>>> 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. >>> >> >> 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. > > Try to crank a car with it! > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������To some extent. you are both ignoring the fact that energy is not power and are using the terms interchangably. Clearly a charged 6-volt car battery (can it still hold a charge after so many years?) holds much nore energy than a 9-volt transistor radio battery. However if you put 1 ohm resistors across both, the one attached to the 9-volt battery will get warmer, at least for a short while. That said, the voltage (or power into into a resistor) of a D/A converter depends on the D/A converter. A sequence of numbers chosen at random, say [1,2,3,4,5], could output [1,2,3,4,5] volts (with some agreed upon sampling rate) or {.001,.002,.003,.004,.005] volts. Of course, the output of a D/A converter doesn't have to be voltage. It could be amps of current, PSI of gas, GPM of water..... Saying that a sequence of numbers has a certain power ignores the implicit scaling factors,
Reply by ●October 3, 20092009-10-03
Remeber that power = voltage*current. The 6volt battery is probably capable of supplying 100amps to start your car but the 9volt battery which is probably a pp3? will probably start complaining if you try to draw more than 1 amp from it. That's a big difference in the power they can supply. The capacity of a battery is usually expressed in amp hours so a 10 amp hour battery can supply 1 amp for 10 hours. The car battery will have allot more capacity than the pp3 so it can supply allot more power for a longer period. The official definition of power is work over time isn't it?
Reply by ●October 3, 20092009-10-03
On Oct 3, 8:20�am, "Nikhil A D" <nikhil2...@gmail.com> wrote:> >> (...) > >> 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. > > 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. > > NikhilThat's an interesting point because now you have defined an impedance that you can use to calculate power. Thing is, the 1 ohm resistor doesn't exist you are just using it as a convenience to figure out what would happen if it was there. The digital signal itself is not dissipating any power across a resistor.
