An apparatus for fabricating new discrete-time data samples from existing discrete-time data samples, comprising: an input line for accepting an input signal; a plurality of processing branches (145B, 155B, 165B, 175B) coupled to the input line, each of said processing branches including: (a) a branch input coupled to the input line and inputting input samples that are discrete in time and value; (b) a downconverter, (366A and 366B), having an input coupled to the branch input, that uses sine and cosine sequences to convert an intermediate-frequency input into complex-valued data samples represented by quadrature baseband and in-phase baseband outputs, (c) a first lowpass filter coupled to the quadrature baseband output of the downconverter; (d) a second lowpass filter coupled to the in-phase baseband output of the downconverter; (e) a first interpolator coupled to an output of the first lowpass filter, (f) a second interpolator coupled to an output of the second lowpass filter, and (g) a quadrature upconverter (369A, 369B, and 370) that uses sine and cosine sequences to convert complex-valued data samples represented by baseband outputs of the first and second interpolators into an intermediate-frequency output; and an adder coupled to outputs of the plurality of processing branches, wherein different ones of the plurality of processing branches operate at different intermediate frequencies, wherein a phase rotation (342, 343, 680), in an amount based on a variable interpolant value, is applied to the complex-valued data samples originating from the downconverter, and wherein the input samples and output samples of at least one of the plurality of processing branches are different discrete-time representations of an underlying continuous-time signal, with the output samples representing an altered sampling period, as compared to the input samples, and with the sampling period being altered by an amount that depends on the variable interpolant value. an input line for accepting an input signal; a plurality of processing branches (145B, 155B, 165B, 175B) coupled to the input line, each of said processing branches including: (a) a branch input coupled to the input line and inputting input samples that are discrete in time and value; (b) a downconverter, (366A and 366B), having an input coupled to the branch input, that uses sine and cosine sequences to convert an intermediate-frequency input into complex-valued data samples represented by quadrature baseband and in-phase baseband outputs, (c) a first lowpass filter coupled to the quadrature baseband output of the downconverter; (d) a second lowpass filter coupled to the in-phase baseband output of the downconverter; (e) a first interpolator coupled to an output of the first lowpass filter, (f) a second interpolator coupled to an output of the second lowpass filter, and (g) a quadrature upconverter (369A, 369B, and 370) that uses sine and cosine sequences to convert complex-valued data samples represented by baseband outputs of the first and second interpolators into an intermediate-frequency output; and an adder coupled to outputs of the plurality of processing branches, wherein different ones of the plurality of processing branches operate at different intermediate frequencies, wherein a phase rotation (342, 343, 680), in an amount based on a variable interpolant value, is applied to the complex-valued data samples originating from the downconverter, and wherein the input samples and output samples of at least one of the plurality of processing branches are different discrete-time representations of an underlying continuous-time signal, with the output samples representing an altered sampling period, as compared to the input samples, and with the sampling period being altered by an amount that depends on the variable interpolant value.