Quadratic Correlation Filters have recently been used for Automatic Target Recognition (ATR). Among these, the Rayleigh Quotient Quadratic Correlation Filter (RQQCF) was found to give excellent performance when tested extensively with Infrared imagery. In the RQQCF method, the filter coefficients are obtained, from a set of training images, such that the response to the filter is large when the input is a target and small when the input is clutter. The method explicitly maximizes a class separation metric to obtain optimal performance. In this paper, a novel transform domain approach is presented for ATR using the RQQCF. The proposed approach, called the Transform Domain RQQCF (TDRQQCF) considerably reduces the computational complexity and storage requirements, by compressing the target and clutter data used in designing the QCF. Since the dimensionality of the data points is reduced, this method also overcomes the common problem of dealing with low rank matrices arising from the lack of large training sets in practice. This is achieved while retaining the high recognition accuracy of the original RQQCF technique. The proposed method is tested using IR imagery, and sample results are presented which confirm its excellent properties.