Delta-rational chord: Difference between revisions

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which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''1:''r''2:...:''r''''n'' chord by α in order to compare it to the target DR chord on the same isodifferential series.)

This error measure is called '''least-squares ~~linear~~ error'''{{idiosyncratic}} (~~LSL~~ error)~~, where "linear" refers to linear frequency domain as opposed to logarithmic~~. As ~~LSL~~ error does not depend on whether the chord whose error is being measured is 1:''r''1:''r''2:...:''r''''n'' or the same chord linearly shifted to have root α, it can be used as a distance function between two delta signatures with no free terms, called '''least-squares ~~linear~~ distance'''.

This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). As LSD error does not depend on whether the chord whose error is being measured is 1:''r''1:''r''2:...:''r''''n'' or the same chord linearly shifted to have root α, it can be used as a distance function between two delta signatures with no free terms, called '''least-squares delta distance'''.

==== Partially DR ====

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 which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> chord by α in order to compare it to the target DR chord on the same isodifferential series.)
-This error measure is called '''least-squares linear error'''{{idiosyncratic}} (LSL error), where "linear" refers to linear frequency domain as opposed to logarithmic. As LSL error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α, it can be used as a distance function between two delta signatures with no free terms, called '''least-squares linear distance'''.
+This error measure is called '''least-squares delta error'''{{idiosyncratic}} (LSD error). As LSD error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α, it can be used as a distance function between two delta signatures with no free terms, called '''least-squares delta distance'''.
 ==== Partially DR ====