Reducing sample frequencies in measurement systems can save power, but reduction to the point of undersampling results in aliasing and possible signal distortion. Nonlinearities of the system under test can also lead to distortions prior to measurement. In this dissertation, a first algorithm is presented for designing multisine excitation signals that can be undersampled without distortion from the aliasing of excitation frequencies or select harmonics. Next, a second algorithm is presented for designing undersampled distributions that approximate target frequency distributions. Results for pseudo-logarithmically-spaced frequency distributions designed for undersampling without distortion from select harmonics show a considerable decrease in the required sampling frequency and an improvement in the discrete Fourier transform (DFT) bin utilization compared to similar Nyquist-sampled output signals. Specifically, DFT bin utilization is shown to improve by eleven-fold when the second algorithm is applied to a 25 tone target logarithmic-spaced frequency distribution that can be applied to a nonlinear system with 2nd and 3rd order harmonics without resulting in distortion of the excitation frequencies at the system output. This dissertation also presents a method for optimizing the generation of multisine excitation signals to allow for significant simplifications in hardware. The proposed algorithm demonstrates that a summation of square waves can sufficiently approximate a target multisine frequency distribution while simultaneously optimizing the frequency distribution to prevent corruption from some non-fundamental harmonic frequencies. Furthermore, a technique for improving the crest factor of a multisine signal composed of square waves shows superior results compared to random phase optimization, even when the set of obtainable signal phases is restricted to a limited set to further reduce hardware complexity.