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Extended Convolution Techniques for Cross-SynthesisCross-synthesis, the ability to blend the spectral characteristics of two sounds together, is an alluring prospect. Often, the go-to technique to accomplish this task is discrete convolution. When using convolution for cross-synthesis, one of the two sounds is treated as a finite impulse response filter and applied to the other. The resultant hybrid sound can be said to possess characteristics of both of the originals. The process is inflexible however and gives the musician no control over the outcome other than by manipulating the sources. We introduce novel extensions to the discrete convolution operation to give musicians more control over the process. We also analyze the implications of discrete convolution and our extensions on high-level acoustic features using a curated dataset of "random" sounds.