A waveform generator, comprising: a splitter structured to receive a digital input signal having an input signal frequency bandwidth and structured to split the digital input signal into a plurality of split signals, each of the split signals having a split signal frequency bandwidth that is substantially similar to the input signal frequency bandwidth; a plurality of digital harmonic mixers structured to digitally mix an associated one of the split signals with an associated digital harmonic signal of a plurality of digital harmonic signals to generate a plurality of digital mixed signals; wherein each associated digital harmonic signal of the plurality of digital harmonic signals includes at least a zero-order harmonic and a first order harmonic signal; wherein the first order harmonic signals are equally spaced in phase by time shifts of one period divided by the number of split signals; a plurality of digital to analog converters, each of the plurality of digital to analog converters structured to convert an associated digital mixed signal of the plurality of digital mixed signals to an analog signal, each of the digital to analog converters having an effective sample rate that is different from the first order harmonic signal of at least one of the associated digital harmonic mixers; a plurality of analog harmonic mixers structured to mix an associated one of the analog signals with an associated analog harmonic signal of a plurality of analog harmonic signals to generate a plurality of mixed, analog signals; and wherein each associated analog harmonic signal of the plurality of analog harmonic signals includes at least a zero-order harmonic and the first order harmonic signal; a combiner structured to combine the plurality of mixed, analog signals into an output signal having an output signal bandwidth that is greater than a bandwidth of at least one of the plurality of digital to analog converters; a plurality of symmetric digital filters that are structured to filter the plurality of digital mixed signals before the digital mixed signals are converted to analog signals; wherein the first-order harmonic of the at least one harmonic signal associated with the digital harmonic mixers is between the effective sample rate of the at least one of the digital to analog converters and one half the effective sample rate of the at least one of the digital to analog converters. a splitter structured to receive a digital input signal having an input signal frequency bandwidth and structured to split the digital input signal into a plurality of split signals, each of the split signals having a split signal frequency bandwidth that is substantially similar to the input signal frequency bandwidth; a plurality of digital harmonic mixers structured to digitally mix an associated one of the split signals with an associated digital harmonic signal of a plurality of digital harmonic signals to generate a plurality of digital mixed signals; wherein each associated digital harmonic signal of the plurality of digital harmonic signals includes at least a zero-order harmonic and a first order harmonic signal; wherein the first order harmonic signals are equally spaced in phase by time shifts of one period divided by the number of split signals; a plurality of digital to analog converters, each of the plurality of digital to analog converters structured to convert an associated digital mixed signal of the plurality of digital mixed signals to an analog signal, each of the digital to analog converters having an effective sample rate that is different from the first order harmonic signal of at least one of the associated digital harmonic mixers; a plurality of analog harmonic mixers structured to mix an associated one of the analog signals with an associated analog harmonic signal of a plurality of analog harmonic signals to generate a plurality of mixed, analog signals; and wherein each associated analog harmonic signal of the plurality of analog harmonic signals includes at least a zero-order harmonic and the first order harmonic signal; a combiner structured to combine the plurality of mixed, analog signals into an output signal having an output signal bandwidth that is greater than a bandwidth of at least one of the plurality of digital to analog converters; a plurality of symmetric digital filters that are structured to filter the plurality of digital mixed signals before the digital mixed signals are converted to analog signals; wherein the first-order harmonic of the at least one harmonic signal associated with the digital harmonic mixers is between the effective sample rate of the at least one of the digital to analog converters and one half the effective sample rate of the at least one of the digital to analog converters.