Single cell whole-genome sequencing (scWGS) is providing novel insights into the nature of genetic heterogeneity in normal and diseased cells. However, the whole-genome amplification process required for scWGS introduces biases into the resulting sequencing that can confound downstream analysis. Here, we present a statistical method, with an accompanying package PaSD-qc (Power Spectral Density-qc), that evaluates the properties and quality of single cell libraries. It uses a modified power spectral density to assess amplification uniformity, amplicon size distribution, autocovariance and inter-sample consistency as well as to identify chromosomes with aberrant read-density profiles due either to copy alterations or poor amplification. These metrics provide a standard way to compare the quality of single cell samples as well as yield information necessary to improve variant calling strategies. We demonstrate the usefulness of this tool in comparing the properties of scWGS protocols, identifying potential chromosomal copy number variation, determining chromosomal and subchromosomal regions of poor amplification, and selecting high-quality libraries from low-coverage data for deep sequencing. The software is available free and open-source at https://github.com/parklab/PaSDqc.