an apparatus for frequency synchronization is proposed to detect a synchronization signal from the baseband signals . it is featured that three types of detection values are introduced to detect whether the synchronization signal is received or not . more particularly , the claimed frequency synchronization apparatus provides at least one signal power generator for receiving a predetermined number of symbols of the baseband signals , and further calculating an average quality value therefore . further , the apparatus includes a signal selector for producing a first detection value according to the average quality value . still further , the apparatus provides a decision unit to produce a second detection value . after that , a signal processor inside the decision unit is used to calculate a third detection value as combining the first detection value and the second detection . consequently , the decision unit particularly decides whether the synchronization signal is received or not in reference with the third detection value .