An apparatus for detecting a tone signal in a telephone switching system is provided in which a calculation, in particular, multiplication is performed by a table look-up process in a digital memory, instead of using a conventional complicated multiplier. A tone signal of a particular frequency in a telephone line is detected through a discrete Fourier transform process (DFT), by the calculation of s(i)=x(iT).times.sin(i2.pi.fT), c(i)=x(iT).times.cos(i2.pi.fT), S=.SIGMA.s(i), C=.SIGMA.c(i), and P=S.sup.2 +C.sup.2. In the above calculation, the multiplication (x(iT).times.sin(i2.pi.fT), and x(iT).times.cos(i2.pi.fT)) is performed by a table look up method in a read only memory (ROM). Thus, the calculation is simplified. Further, the ROM has cells for only the discrete particular levels of multiplicands and/or the multipliers to reduce the capacity of the ROM, and the ROM is referred to by the multiplicand and/or the multiplier through the conversion of the same by a coefficient number generator.