For a digital demodulator for AM demodulation of a difference sound signal in a digital multiplex signal, which multiplex signal also comprises a sum sound signal in the baseband position and a pilot carrier at a pilot frequency, and the difference sound signal is modulated on a carrier at twice the pilot frequency, an extremely simple and adjustment-free construction is ensured in that CORDICs (1, 7) are provided which perform a coordinate transformation of polar coordinates into cartesian coordinates and each have a phase input, two amplitude inputs assigned to the coordinates x and y and two outputs assigned to the coordinates x and y, in that a phase-locked loop comprising a first CORDIC (1), a loop filter (2) and an accumulator (4) are provided, which phase-locked loop supplies a phase ramp signal whose repetition frequency is dependent on the input signal of the accumulator, in that the multiplex signal at an amplitude input of the first CORDIC (1), the output signal of the accumulator (4) at the phase input of the first CORDIC (1) and that output of the first CORDIC (1) which is not assigned to the same coordinate as the amplitude input used are applied to the loop filter (4) whose output signal is superimposed by means of a first superposition stage (3) on a frequency selection signal indicating a pilot nominal frequency, and the output signal of the superposition stage (3) is applied to the accumulator input (4), in that a second CORDIC (7) is provided, one amplitude input of which receives the multiplex signal with the suppressed pilot and the phase input of which receives the output signal from a multiplier (5) whose input receives the output signal from the accumulator (4) and multiplies said output signal by a factor of two, and in that the output of the second CORDIC (7) supplies the demodulated difference sound signal.