The success of deep learning-based generative models in producing realistic images, videos, and audios has led to a crucial consideration: how to effectively assess the quality of synthetic samples. While the Fr\'{e}chet Inception Distance (FID) serves as the standard metric for evaluating generative models in image synthesis, a comparable metric for time series data is notably absent. This gap in assessment capabilities stems from the absence of a widely accepted feature vector extractor pre-trained on benchmark time series datasets. In addressing these challenges related to assessing the quality of time series, particularly in the context of Fr\échet Distance, this work proposes a novel solution leveraging the Fourier transform and Auto-encoder, termed the Fr\'{e}chet Fourier-transform Auto-encoder Distance (FFAD). Through our experimental results, we showcase the potential of FFAD for effectively distinguishing samples from different classes. This novel metric emerges as a fundamental tool for the evaluation of generative time series data, contributing to the ongoing efforts of enhancing assessment methodologies in the realm of deep learning-based generative models.
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