Timeline for Why Decibels are used to measure Signal to Noise Ratio?
Current License: CC BY-SA 3.0
18 events
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| Sep 24, 2013 at 15:33 | history | edited | Vorac | CC BY-SA 3.0 |
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| Sep 24, 2013 at 15:11 | comment | added | supercat | @kriss: If one has an RC network, one may describe the network without knowing frequency by adding together resistances, capacitances, inductances, and their reciprocals. The units don't reduce unless one can apply a particular frequency, but I think one can perform the arithmetic without knowing the frequency, keeping things as discrete units, and then turn inductances and capacitances into impedances afterward. | |
| Sep 23, 2013 at 23:35 | comment | added | kriss | @supercat: you are not adding ohms and Farad, you do that at some given Frenquency in termes of units you have (Ω = F * s).That's Buckingham π theorem. It's handy to check some result (if dimensions does not match result is false). But it says nothing on dimensionless units. I'm not sure either about Torque and Energy, but from a pure units point of view it could have a meaning as units match. | |
| Sep 23, 2013 at 23:13 | comment | added | supercat | @kriss: How about adding one ohm to one farad? Those are different dimensions, but the sum is meaningful; it effectively describes a relationship between frequency and complex impedance. I'm not quite sure what a sum of torque and energy would mean, but if one regards a unit of torque as being a vector perpendicular to a unit of energy, and a radian as being "perpendicular" to a unit distance, then the rotation of something by one radian against a certain (force times distance) torque will require the (force times distance) amount of work. | |
| Sep 23, 2013 at 22:41 | comment | added | kriss | @supercat: all units of length are of the same dimension, whatever you name them. But you can't add 1 volt and 1 meter. It means nothing. With dimensionless units you are exactly as meaningful adding say 1 rad and 360 degrees, you obviously get 2Pi+1 rad. But obviously adding Db is meaningless. And I don't see what would be the meaning of adding say some angle and some Atomic Weight, even if both are dimensionless. | |
| Sep 23, 2013 at 15:30 | comment | added | supercat | @kriss: Adding 1 inch and one foot is perfectly meaningful; without conversion the answer is "1 inch + 1 foot". Multiply the right half by the identity "12 inch / 1 foot" and it becomes "1 inch + 12 inch", which can then be reduced to "13 inch". | |
| Sep 20, 2013 at 23:14 | comment | added | kriss | @supercat: OK. Having the same unit is not enough. But still, as far as I know adding units with different dimensions is always meaningless. And it also seems you can't always mix dimensionless units. But maybe I's rather ask a question on that subject on physics stackexchange. | |
| Sep 20, 2013 at 22:52 | comment | added | supercat | @kriss: Pretty much. If someone walks 12 meters, and then walks 9 meters, how far from their starting point will they end up? Only if all 21 meters are traversed in the same direction can one answer the question by adding the distances. | |
| Sep 20, 2013 at 22:31 | comment | added | kriss | @supercat: I'm not sure I understand the point. Do you mean that we can have units with defined dimensions but that you can't meaningfully add ? (because we should add them as vectors and that is only defined when vectors point in the same direction ?) | |
| Sep 20, 2013 at 20:58 | comment | added | supercat | @kriss: The terms "unit" and "dimension" are a bit vague. Consider, for example, the difference between "one pound foot" (a measure of torque) vs. "one foot pound" (a measure of energy). Both force and distance are properly described as vectors which have associated directions. When describing "one pound foot", the vectors point in arbitrary perpendicular directions; when describing energy, they point in the same arbitrary direction. | |
| Sep 20, 2013 at 12:47 | comment | added | kriss | @Vorac: as far as I understand radians are dimensionless, but not unitless. Both are not exactly synonyms. Radian are always a mesure of an angle, which is physically defined. dB are not physically defined in the same way: that's some log representation of the ratio of two intensities, but it does not state the intensities of what. | |
| Sep 20, 2013 at 10:09 | comment | added | MSalters | You can take the sine of one radian. That in itself is proof of the fact that they are unit-less. To convince yourself, look at the Taylor expansion of sin(x). If x has a unit, you're calculating x-(x^3/6). | |
| Sep 20, 2013 at 9:15 | comment | added | Vorac | @kriss, yea, but by definition, the angle of radians is the ratio of the arc, divided by the radius. I am getting confused now! | |
| Sep 20, 2013 at 3:07 | comment | added | kriss | actually radians are not unitless. They are a unit of measure of angle, like meter is a unit of mesure of length. Unitless quantities are generally coefficients that are applied to convert between units, including of course db. | |
| Sep 19, 2013 at 16:11 | comment | added | AndrejaKo | Natural logarithm is actually used for unit called neper (Np). | |
| Sep 19, 2013 at 14:06 | comment | added | Vorac | @Andy aka, right you are! | |
| Sep 19, 2013 at 14:04 | comment | added | Andy aka | I think you should use log not ln to calculate decibels | |
| Sep 19, 2013 at 14:02 | history | answered | Vorac | CC BY-SA 3.0 |