Correlation filters are attractive for automatic target recognition (ATR) applications due to such attributes as shift invariance, distortion tolerance and graceful degradation. Composite correlation filters are designed to handle target distortions by training on a set of images that represent the expected distortions during testing. However, if the distortion can be described algebraically, as in the case of in-plane rotation and scale, then only one training image is necessary. A recently introduced scale-tolerant correlation filter design, called the Minimum Average Correlation Energy Mellin Radial Harmonic (MACE-MRH) filter, exploits this algebraic property and allows the user to specify the scale response of the filter. These filters also minimize the average correlation energy in order to help control the sidelobes in the correlation output and produce sharper, more detectable peaks. In this paper we show that applying non-linearities in the frequency domain (leading to fractional power scale-tolerant correlation filters) can significantly improve the resulting peak sharpness, yielding larger peak-to-correlation energy values for true-class targets at various scales in a scene image. We investigate the effects of fractional power transformations on MACE-MRH filter performance by using a testbed of fifty video sequences consisting of long-wave infrared (LWIR) imagery, in which the observer moves along a flight path toward one or more ground targets of interest. Targets in the test sequences suffer large amounts of scale distortion due to the approach trajectory of the camera. MACE-MRH filter banks are trained on single targets and applied to each sequence on a frame-by-frame basis to perform target detection and recognition. Recognition results from both fractional power MACE-MRH filters and regular MACE-MRH filters are provided, showing the improvement in scale-tolerant recognition from applying fractional power non-linearities to these filters.