@section Logarithmic Units
The units @code{dB} (decibels) and @code{Np} (nepers) are logarithmic
-units which are typically manipulated differently than standard units.
-Calc provides commands to work with these logarithmic units.
+units which are manipulated differently than standard units. Calc
+provides commands to work with these logarithmic units.
Decibels and nepers are used to measure power quantities as well as
-field quantities (quantities whose squares are proportional to power).
-The decibel and neper values of a quantity are relative to
-a reference quantity; for example, the decibel value of a sound
-pressure level of
-@infoline @math{60 uPa}
-@texline @math{60 \mu{\rm Pa}}
-relative to
-@infoline @math{20 uPa}
-@texline @math{20 \mu{\rm Pa}}
-(the threshhold of human hearing) is
-@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB},
-@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}},
-which is about
-@infoline @math{9.54 dB}.
-@texline @math{9.54 {\rm dB}}.
-Note that in taking the ratio, the original units cancel and so these
-logarithmic units are dimensionless.
-
-@vindex calc-logunits-power-reference
-@vindex calc-logunits-field-reference
-The Calc commands for the logarithmic units assume that power quantities
-are being used unless the @kbd{H} prefix is used, in which case they assume that
-field quantities are being used. For power quantities, Calc uses
-@infoline @math{1 mW}
-@texline @math{1 {\rm mW}}
-as the default reference quantity; this default can be changed by changing
-the value of the customizable variable
-@code{calc-logunits-power-reference} (@pxref{Customizing Calc}).
-For field quantities, Calc uses
-@infoline @math{20 uPa}
-@texline @math{20 \mu{\rm Pa}}
-as the default reference quantity; this is the value used in acoustics
-which is where decibels are commonly encountered. This default can be
-changed by changing the value of the customizable variable
-@code{calc-logunits-field-reference} (@pxref{Customizing Calc}). A
-non-default reference quantity will be read from the stack if the
-capital @kbd{O} prefix is used.
+field quantities (quantities whose squares are proportional to power);
+these two types of quantities are handled slightly different from each
+other. By default the Calc commands work as if power quantities are
+being used; with the @kbd{H} prefix the Calc commands work as if field
+quantities are being used.
The decibel level of a power
@infoline @math{P1},
is defined as
@infoline @math{20 log10(F1/F0) dB}.
@texline @math{20 \log_{10}(F_{1}/F_{0}) {\rm dB}}.
+For example, the decibel value of a sound pressure level of
+@infoline @math{60 uPa}
+@texline @math{60 \mu{\rm Pa}}
+relative to
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+(the threshhold of human hearing) is
+@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB},
+@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}},
+which is about
+@infoline @math{9.54 dB}.
+@texline @math{9.54 {\rm dB}}.
+Note that in taking the ratio, the original units cancel and so these
+logarithmic units are dimensionless.
Nepers (named after John Napier, who is credited with inventing the
logarithm) are similar to bels except they use natural logarithms instead
@infoline @math{ln(F1/F0) Np}.
@texline @math{\ln(F_1/F_0) {\rm Np}}.
+@vindex calc-lu-power-reference
+@vindex calc-lu-field-reference
+For power quantities, Calc uses
+@infoline @math{1 mW}
+@texline @math{1 {\rm mW}}
+as the default reference quantity; this default can be changed by changing
+the value of the customizable variable
+@code{calc-lu-power-reference} (@pxref{Customizing Calc}).
+For field quantities, Calc uses
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+as the default reference quantity; this is the value used in acoustics
+which is where decibels are commonly encountered. This default can be
+changed by changing the value of the customizable variable
+@code{calc-lu-field-reference} (@pxref{Customizing Calc}). A
+non-default reference quantity will be read from the stack if the
+capital @kbd{O} prefix is used.
+
@kindex l q
-@pindex calc-logunits-quantity
-@tindex powerquant
-@tindex fieldquant
-The @kbd{l q} (@code{calc-logunits-quantity}) [@code{powerquant}]
+@pindex calc-lu-quant
+@tindex pquant
+@tindex fquant
+The @kbd{l q} (@code{calc-lu-quant}) [@code{pquant}]
command computes the power quantity corresponding to a given number of
logarithmic units. With the capital @kbd{O} prefix, @kbd{O l q}, the
reference level will be read from the top of the stack. (In an
-algebraic formula, @code{powerquant} can be given an optional second
+algebraic formula, @code{pquant} can be given an optional second
argument which will be used for the reference level.) For example,
@code{20 dB @key{RET} l q} will return @code{100 mW};
@code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}.
-The @kbd{H l q} [@code{fieldquant}] command behaves like @kbd{l q} but
+The @kbd{H l q} [@code{fquant}] command behaves like @kbd{l q} but
computes field quantities instead of power quantities.
@kindex l d
-@pindex calc-dblevel
-@tindex dbpowerlevel
-@tindex dbfieldlevel
+@pindex calc-db
+@tindex dbpower
+@tindex dbfield
@kindex l n
-@pindex calc-nplevel
-@tindex nppowerlevel
-@tindex npfieldlevel
-The @kbd{l d} (@code{calc-dblevel}) [@code{dbpowerlevel}]
-command will compute the decibel level of a power quantity using the
-default reference level; @kbd{H l d} [@code{dbfieldlevel}] will
-compute the decibel level of a field quantity. The commands @kbd{l n}
-(@code{calc-nplevel}) [@code{nppowerlevel}] and @kbd{H l n}
-[@code{npfieldlevel}] will similarly compute neper levels. With the
-capital @kbd{O} prefix these commands will read a reference level
-from the stack; in an algebraic formula the reference level can be
-given as an optional second argument.
+@pindex calc-np
+@tindex nppower
+@tindex npfield
+The @kbd{l d} (@code{calc-db}) [@code{dbpower}] command will compute
+the decibel level of a power quantity using the default reference
+level; @kbd{H l d} [@code{dbfield}] will compute the decibel level of
+a field quantity. The commands @kbd{l n} (@code{calc-np})
+[@code{nppower}] and @kbd{H l n} [@code{npfield}] will similarly
+compute neper levels. With the capital @kbd{O} prefix these commands
+will read a reference level from the stack; in an algebraic formula
+the reference level can be given as an optional second argument.
@kindex l +
-@pindex calc-logunits-add
-@tindex lupoweradd
-@tindex lufieldadd
+@pindex calc-lu-plus
+@tindex lupadd
+@tindex lufadd
@kindex l -
-@pindex calc-logunits-sub
-@tindex lupowersub
-@tindex lufieldsub
+@pindex calc-lu-minus
+@tindex lupsub
+@tindex lufsub
@kindex l *
-@pindex calc-logunits-mul
-@tindex lupowermul
-@tindex lufieldmul
+@pindex calc-lu-times
+@tindex lupmul
+@tindex lufmul
@kindex l /
-@pindex calc-logunits-div
-@tindex lupowerdiv
-@tindex lufielddiv
+@pindex calc-lu-divide
+@tindex lupdiv
+@tindex lufdiv
The sum of two power or field quantities doesn't correspond to the sum
of the corresponding decibel or neper levels. If the powers
corresponding to decibel levels
@end tex
@noindent
-When field quantities are combined, it often means the
-corresponding powers are added and so the above formula might be used.
-In acoustics, for example, the decibel sound pressure level is defined
-using the field formula but the sound pressure levels are combined
-as the sound power levels, and so the above formula should be used. If
-two field quantities themselves are added, the new decibel level will be
-
+When field quantities are combined, it often means the corresponding
+powers are added and so the above formula might be used. In
+acoustics, for example, the sound pressure level is a field quantity
+and so the decibels are often defined using the field formula, but the
+sound pressure levels are combined as the sound power levels, and so
+the above formula should be used. If two field quantities themselves
+are added, the new decibel level will be
@ifnottex
@example
@end tex
@noindent
-There are similar formulas for combining nepers.
-The @kbd{l +} (@code{calc-logunits-add}) [@code{lupoweradd}] command
-will ``add'' two logarithmic unit power levels this way; with the
-@kbd{H} prefix, @kbd{H l +} [@code{lufieldadd}] will add logarithmic
-unit field levels. Similarly, logarithmic units can be
-``subtracted'' with @kbd{l -} (@code{calc-logunits-sub})
-[@code{lupowersub}] or @kbd{H l -} [@code{lufieldsub}].
-The @kbd{l *} (@code{calc-logunits-mul}) [@code{lupowermul}]
-and @kbd{H l *} [@code{lufieldmul}] commands will ``multiply''
-a logarithmic unit by a number; the @kbd{l /}
-(@code{calc-logunits-divide}) [@code{lupowerdiv}] and
-@kbd{H l /} [@code{lufielddiv}] commands will ``divide'' a
-logarithmic unit by a number. Note that the reference quantities don't
-play a role in this arithmetic.
+There are similar formulas for combining nepers. The @kbd{l +}
+(@code{calc-lu-plus}) [@code{lupadd}] command will ``add'' two
+logarithmic unit power levels this way; with the @kbd{H} prefix,
+@kbd{H l +} [@code{lufadd}] will add logarithmic unit field levels.
+Similarly, logarithmic units can be ``subtracted'' with @kbd{l -}
+(@code{calc-lu-minus}) [@code{lupsub}] or @kbd{H l -} [@code{lufsub}].
+The @kbd{l *} (@code{calc-lu-times}) [@code{lupmul}] and @kbd{H l *}
+[@code{lufmul}] commands will ``multiply'' a logarithmic unit by a
+number; the @kbd{l /} (@code{calc-lu-divide}) [@code{lupdiv}] and
+@kbd{H l /} [@code{lufdiv}] commands will ``divide'' a logarithmic
+unit by a number. Note that the reference quantities don't play a role
+in this arithmetic.
@node Musical Notes, , Logarithmic Units, Units
@section Musical Notes
and @code{calc-embedded-open-close-plain-alist}.
@end defvar
-@defvar calc-logunits-power-reference
-@defvarx calc-logunits-field-reference
+@defvar calc-lu-power-reference
+@defvarx calc-lu-field-reference
See @ref{Logarithmic Units}.@*
-The variables @code{calc-logunits-power-reference} and
-@code{calc-logunits-field-reference} are unit expressions (written as
+The variables @code{calc-lu-power-reference} and
+@code{calc-lu-field-reference} are unit expressions (written as
strings) which Calc will use as reference quantities for logarithmic
units.
-The default value of @code{calc-logunits-power-reference} is @code{"mW"}
-and the default value of @code{calc-logunits-field-reference} is
+The default value of @code{calc-lu-power-reference} is @code{"mW"}
+and the default value of @code{calc-lu-field-reference} is
@code{"20 uPa"}.
@end defvar
@r{ v x@: I k T @: @: @:ltpt@:(x,v)}
@c
-@r{ a b@: l + @: @: @:lupoweradd@:(a,b)}
-@r{ a b@: H l + @: @: @:lufieldadd@:(a,b)}
-@r{ a b@: l - @: @: @:lupowersub@:(a,b)}
-@r{ a b@: H l - @: @: @:lufieldsub@:(a,b)}
-@r{ a b@: l * @: @: @:lupowermul@:(a,b)}
-@r{ a b@: H l * @: @: @:lufieldmul@:(a,b)}
-@r{ a b@: l / @: @: @:lupowerdiv@:(a,b)}
-@r{ a b@: H l / @: @: @:lufielddiv@:(a,b)}
-@r{ a@: l d @: @: @:dbpowerlevel@:(a)}
-@r{ a b@: O l d @: @: @:dbpowerlevel@:(a,b)}
-@r{ a@: H l d @: @: @:dbfieldlevel@:(a)}
-@r{ a b@: O H l d @: @: @:dbfieldlevel@:(a,b)}
-@r{ a@: l n @: @: @:nppowerlevel@:(a)}
-@r{ a b@: O l n @: @: @:nppowerlevel@:(a,b)}
-@r{ a@: H l n @: @: @:npfieldlevel@:(a)}
-@r{ a b@: O H l n @: @: @:npfieldlevel@:(a,b)}
-@r{ a@: l q @: @: @:powerquant@:(a)}
-@r{ a b@: O l q @: @: @:powerquant@:(a,b)}
-@r{ a@: H l q @: @: @:fieldquant@:(a)}
-@r{ a b@: O H l q @: @: @:fieldquant@:(a,b)}
+@r{ a b@: l + @: @: @:lupadd@:(a,b)}
+@r{ a b@: H l + @: @: @:lufadd@:(a,b)}
+@r{ a b@: l - @: @: @:lupsub@:(a,b)}
+@r{ a b@: H l - @: @: @:lufsub@:(a,b)}
+@r{ a b@: l * @: @: @:lupmul@:(a,b)}
+@r{ a b@: H l * @: @: @:lufmul@:(a,b)}
+@r{ a b@: l / @: @: @:lupdiv@:(a,b)}
+@r{ a b@: H l / @: @: @:lufdiv@:(a,b)}
+@r{ a@: l d @: @: @:dbpower@:(a)}
+@r{ a b@: O l d @: @: @:dbpower@:(a,b)}
+@r{ a@: H l d @: @: @:dbfield@:(a)}
+@r{ a b@: O H l d @: @: @:dbfield@:(a,b)}
+@r{ a@: l n @: @: @:nppower@:(a)}
+@r{ a b@: O l n @: @: @:nppower@:(a,b)}
+@r{ a@: H l n @: @: @:npfield@:(a)}
+@r{ a b@: O H l n @: @: @:npfield@:(a,b)}
+@r{ a@: l q @: @: @:pquant@:(a)}
+@r{ a b@: O l q @: @: @:pquant@:(a,b)}
+@r{ a@: H l q @: @: @:fquant@:(a)}
+@r{ a b@: O H l q @: @: @:fquant@:(a,b)}
@r{ a@: l s @: @: @:spn@:(a)}
@r{ a@: l m @: @: @:midi@:(a)}
@r{ a@: l f @: @: @:freq@:(a)}
coef)))
units)))))))
-(defun calcFunc-lufieldplus (a b)
+(defun calcFunc-lufadd (a b)
(math-logunits-add a b nil nil))
-(defun calcFunc-lupowerplus (a b)
+(defun calcFunc-lupadd (a b)
(math-logunits-add a b nil t))
-(defun calcFunc-lufieldminus (a b)
+(defun calcFunc-lufsub (a b)
(math-logunits-add a b t nil))
-(defun calcFunc-lupowerminus (a b)
+(defun calcFunc-lupsub (a b)
(math-logunits-add a b t t))
-(defun calc-logunits-add (arg)
+(defun calc-lu-plus (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
- (calc-binary-op "lu-" 'calcFunc-lufieldminus arg)
- (calc-binary-op "lu-" 'calcFunc-lupowerminus arg))
+ (calc-binary-op "lu-" 'calcFunc-lufsub arg)
+ (calc-binary-op "lu-" 'calcFunc-lupsub arg))
(if (calc-is-hyperbolic)
- (calc-binary-op "lu+" 'calcFunc-lufieldplus arg)
- (calc-binary-op "lu+" 'calcFunc-lupowerplus arg)))))
+ (calc-binary-op "lu+" 'calcFunc-lufadd arg)
+ (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
-(defun calc-logunits-sub (arg)
+(defun calc-lu-minus (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
- (calc-binary-op "lu+" 'calcFunc-lufieldplus arg)
- (calc-binary-op "lu+" 'calcFunc-lupowerplus arg))
+ (calc-binary-op "lu+" 'calcFunc-lufadd arg)
+ (calc-binary-op "lu+" 'calcFunc-lupadd arg))
(if (calc-is-hyperbolic)
- (calc-binary-op "lu-" 'calcFunc-lufieldminus arg)
- (calc-binary-op "lu-" 'calcFunc-lupowerminus arg)))))
+ (calc-binary-op "lu-" 'calcFunc-lufsub arg)
+ (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
(defun math-logunits-mul (a b power)
(let (logunit coef units number)
(math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
units)))))))))
-(defun calcFunc-lufieldtimes (a b)
+(defun calcFunc-lufmul (a b)
(math-logunits-mul a b nil))
-(defun calcFunc-lupowertimes (a b)
+(defun calcFunc-lupmul (a b)
(math-logunits-mul a b t))
-(defun calc-logunits-mul (arg)
+(defun calc-lu-times (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
- (calc-binary-op "lu/" 'calcFunc-lufielddiv arg)
- (calc-binary-op "lu/" 'calcFunc-lupowerdiv arg))
+ (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
+ (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
(if (calc-is-hyperbolic)
- (calc-binary-op "lu*" 'calcFunc-lufieldtimes arg)
- (calc-binary-op "lu*" 'calcFunc-lupowertimes arg)))))
+ (calc-binary-op "lu*" 'calcFunc-lufmul arg)
+ (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
-(defun calcFunc-lufielddiv (a b)
+(defun calcFunc-lufdiv (a b)
(math-logunits-divide a b nil))
-(defun calcFunc-lupowerdiv (a b)
+(defun calcFunc-lupdiv (a b)
(math-logunits-divide a b t))
-(defun calc-logunits-divide (arg)
+(defun calc-lu-divide (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
- (calc-binary-op "lu*" 'calcFunc-lufieldtimes arg)
- (calc-binary-op "lu*" 'calcFunc-lupowertimes arg))
+ (calc-binary-op "lu*" 'calcFunc-lufmul arg)
+ (calc-binary-op "lu*" 'calcFunc-lupmul arg))
(if (calc-is-hyperbolic)
- (calc-binary-op "lu/" 'calcFunc-lufielddiv arg)
- (calc-binary-op "lu/" 'calcFunc-lupowerdiv arg)))))
+ (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
+ (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
(defun math-logunits-quant (val ref power)
(let* ((units (math-simplify (math-extract-units val)))
coeff))))
runits)))))
-(defvar calc-logunits-field-reference)
-(defvar calc-logunits-power-reference)
+(defvar calc-lu-field-reference)
+(defvar calc-lu-power-reference)
-(defun calcFunc-fieldquant (val &optional ref)
+(defun calcFunc-fquant (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-field-reference)))
+ (setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-quant val ref nil))
-(defun calcFunc-powerquant (val &optional ref)
+(defun calcFunc-pquant (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-power-reference)))
+ (setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-quant val ref t))
-(defun calc-logunits-quantity (arg)
+(defun calc-lu-quant (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-hyperbolic)
(if (calc-is-option)
- (calc-binary-op "lupq" 'calcFunc-fieldquant arg)
- (calc-unary-op "lupq" 'calcFunc-fieldquant arg))
+ (calc-binary-op "lupq" 'calcFunc-fquant arg)
+ (calc-unary-op "lupq" 'calcFunc-fquant arg))
(if (calc-is-option)
- (calc-binary-op "lufq" 'calcFunc-powerquant arg)
- (calc-unary-op "lufq" 'calcFunc-powerquant arg)))))
+ (calc-binary-op "lufq" 'calcFunc-pquant arg)
+ (calc-unary-op "lufq" 'calcFunc-pquant arg)))))
(defun math-logunits-level (val ref db power)
"Compute the value of VAL in decibels or nepers."
'(var Np var-Np)))
units)))
-(defun calcFunc-dbfieldlevel (val &optional ref)
+(defun calcFunc-dbfield (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-field-reference)))
+ (setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-level val ref t nil))
-(defun calcFunc-dbpowerlevel (val &optional ref)
+(defun calcFunc-dbpower (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-power-reference)))
+ (setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-level val ref t t))
-(defun calcFunc-npfieldlevel (val &optional ref)
+(defun calcFunc-npfield (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-field-reference)))
+ (setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-level val ref nil nil))
-(defun calcFunc-nppowerlevel (val &optional ref)
+(defun calcFunc-nppower (val &optional ref)
(unless ref
- (setq ref (math-read-expr calc-logunits-power-reference)))
+ (setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-level val ref nil t))
-(defun calc-dblevel (arg)
+(defun calc-db (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-hyperbolic)
(if (calc-is-option)
- (calc-binary-op "ludb" 'calcFunc-dbfieldlevel arg)
- (calc-unary-op "ludb" 'calcFunc-dbfieldlevel arg))
+ (calc-binary-op "ludb" 'calcFunc-dbfield arg)
+ (calc-unary-op "ludb" 'calcFunc-dbfield arg))
(if (calc-is-option)
- (calc-binary-op "ludb" 'calcFunc-dbpowerlevel arg)
- (calc-unary-op "ludb" 'calcFunc-dbpowerlevel arg)))))
+ (calc-binary-op "ludb" 'calcFunc-dbpower arg)
+ (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
-(defun calc-nplevel (arg)
+(defun calc-np (arg)
(interactive "P")
(calc-slow-wrapper
(if (calc-is-hyperbolic)
(if (calc-is-option)
- (calc-binary-op "lunp" 'calcFunc-npfieldlevel arg)
- (calc-unary-op "lunp" 'calcFunc-npfieldlevel arg))
+ (calc-binary-op "lunp" 'calcFunc-npfield arg)
+ (calc-unary-op "lunp" 'calcFunc-npfield arg))
(if (calc-is-option)
- (calc-binary-op "lunp" 'calcFunc-nppowerlevel arg)
- (calc-unary-op "lunp" 'calcFunc-nppowerlevel arg)))))
+ (calc-binary-op "lunp" 'calcFunc-nppower arg)
+ (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
;;; Musical notes
projects / emacs.git / commitdiff