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The objective of Aspect Based Sentiment Analysis is to capture the sentiment of reviewers associated with different aspects. However, complexity of the review sentences, presence of double negation and specific usage of words found in different domains make it difficult to predict the sentiment accurately and overall a challenging natural language understanding task. While recurrent neural network, attention mechanism and more recently, graph attention based models are prevalent, in this paper we propose graph Fourier transform based network with features created in the spectral domain. While this approach has found considerable success in the forecasting domain, it has not been explored earlier for any natural language processing task. The method relies on creating and learning an underlying graph from the raw data and thereby using the adjacency matrix to shift to the graph Fourier domain. Subsequently, Fourier transform is used to switch to the frequency (spectral) domain where new features are created. These series of transformation proved to be extremely efficient in learning the right representation as we have found that our model achieves the best result on both the SemEval-2014 datasets, i.e., "Laptop" and "Restaurants" domain. Our proposed model also found competitive results on the two other recently proposed datasets from the e-commerce domain.