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In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
ln (r) is the standard natural logarithm of the real number r. Arg (z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg (x + iy) = atan2 (y, x). Log (z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
contrast ratio = antilog ( D max. — D min.) If this is applied to the well-known B.B.C. Test Card 'C', we find that, in the positive film version of the card, the maximum density is 2.0 whilst the minimum density is 0.3. Therefore the contrast ratio is as follows: contrast ratio = antilog (2.0 — 0.3) = antilog (1.7)
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer.
Log amplifier. A log amplifier, also known as logarithmic amplifier or logarithm amplifier or log amp, is an amplifier for which the output voltage Vout is K times the natural log of the input voltage Vin. This can be expressed as, where Vref is the normalization constant in volts and K is the scale factor.
Discrete logarithm. In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm log b a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = ind r a ...
The Blackmer cell is a direct descendant of a two-transistor log-antilog circuit, itself a derivative of the simple current mirror.Normally, the bases of two transistors of a mirror are tied together to ensure the collector current I 2 of the output transistor T2 exactly mirrors the collector current I 1 of the input transistor T1.
Blackmer reasoned that the log-antilog detector may be simplified by taking up processing to log domain, omitting physical squaring of input signals and thus retaining its full dynamic range. [3] Squaring and taking square roots in log domain is very cheap, being simple scaling by a factor of 2 or 1/2. [7]