A pulse duration modulated (PDM) signal is generated from a periodic digitized signal which may be produced by sampling an analog signal of frequency F.sub.s and using a digitizing frequency F where F>>F.sub.s. Linearity of the analog signal between sampling points is assumed. A computer solution of the intercept of the assumed straight line between each pair of successive sample values of the digitized signal and a reference triangular waveform of frequency F/2 provides the time interval between intercepts from which the interpolated pulse duration modulated (IPDM) waveform is generated. A method to add low frequency signals in the IPDM domain, useful for providing Class AD amplifiers with a feedback path and for summations of input signals without converting signals back to analog form, operates on the sum of the respective intercept times of each of the signals. The summed intercept times are used to provide an IPDM signal which represents the sum of the original digitized signals. Multiplication of digitized signals in the nonlinear (IPDM) domain is provided by operating on the product of the intercepts of two IPDM signals to obtain the intercepts of a new IPDM signal whose low frequency content is the product of the low frequency component of the two digitized signals. Interpolated signals thus are able to be modulated and frequency shifted in the IPDM domain to improve the linearity of IPDM for higher frequency signals (F not much greater than F.sub.s).
Data from an A/D converter is supplied to a fixed-point DSP. The fixed-point DSP adjusts the level of the data x so that computed results do not exceed .+-.1. In succession, for the i-th data x.sub.i, the fixed-point DSP computes cos .pi..multidot.x.sub.i when i=1, 5, . . . , -sin .pi..multidot.x.sub.i when i=2, 6, . . . , -cos .pi..multidot.x.sub.i when i=3, 7, . . . and sin .pi..multidot.x.sub.i when i=4, 8, . . . and outputs a digital phase modulated signal y(t) by outputting the computed results in order. Trigonometrical functions are computed by expanding them to a series so that the intermediate computed results do not exceed .+-.1.
A digital modulation process and apparatus for converting an input signal comprising a time variable series of sampling values, each of which sampling values remains constant within a fixed sampling period, into output signals representing a sequence of positive and/or negative pulses having a constant amplitude and a variable pulse width and frequency. The input signal and modulator parameters are supplied to a data processor. In order to reduce computing expenditures and at the same time achieve an increase in precision, by means of the computing system, the switch-on and switch-off points in time t.sub.se, t.sub.sa of the pulses as well as their operational signs are computed in one operation directly for each sampling period .DELTA.t.sub.k.
