Abstract: A digital signal processing system applies numbers to the multiplied or divided to address a memory storing a logarithm table to produce the logarithms of the numbers. These logarithms are added for multiplication or substracted for division to produce the logarithm of the result number which is applied to address a memory storing an antilogarithm table to produce the result number. The base of the logarithms is selected in accordance with the magnitudes of the numbers to be multiplied or divided so as to utilize substantially the entire range of magnitudes of the digital representation of the logarithms.

Abstract: In a digital television receiver, a signal processing stage generates color mixture digital signals representing color picture information as components in a first color mixture coordinate system such as the I-Q system. The I and Q digital signals are applied to a read only memory look-up table in which memory locations are stored the logarithmic values of the signals in order to convert the signals into digital words represented in logarithmic form. A microprocessor or other digital circuit generates or retrieves digital coefficients in logarithmic form that enable the I and Q digital signals to be transformed into second color mixture digital signals representing the color picture information as components in a second color mixture coordinate system such as the R-Y, B-Y, color difference coordinate system. The I and Q digital signals in logarithmic form are applied to a first input of an adder.