
Rockbox mail archiveSubject: Re: Power Efficiency TradeoffsRe: Power Efficiency Tradeoffs
From: Mark Allums <mark_at_allums.com>
Date: Mon, 14 Jan 2008 04:36:19 0600 Linus Nielsen Feltzing wrote: > Mike Holden wrote: >> But that's precisely what "proportional" means  linearly proportional! >> >> To be proportional, the two values have to be always at exactly the same >> ratio, such as y = x * 2. > > Well, it can also be exponentially or logarithmically proportional, as > far as I know. > > Linus A proportion is usually written in the form y = kx + c where k is called the "constant of proportionality". A "proportionality" can be expressed by almost any function; the definition of "proportional" however implies a linear function. One possible more "general" equation might be y = F(x) = Px + c where P is some polynomial in some other variable, with P generally a constant, or close to constant, for the range of values we are interested in. This is really a "function" in two variables: e.g., P(q) = s^2 + 2s + 3 y = xs^2 + 2xs + 3x + c If s is close to 1.0 and we can assume it *stays* there, then it becomes y = x + 2x + 3x + c y = 6x + c If it can be represented by an exponential, logarithmic, harmonic or some other function, it is not strictly a "proportion", but that is just nitpicking. It is still useful to make statements like "a is proportional to the square root of b". a = k(b^0.5) + c, where c == 0 And if we *know* the function that approximates the value, we can use it, whatever it is. At any rate, we know what you mean when you say "proportional". :) Mark Allums Received on 20080114 Page template was last modified "Tue Sep 7 00:00:02 2021" The Rockbox Crew  Privacy Policy 