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This letter presents a novel algorithm to compute the instantaneous frequency (IF) of a multicomponent nonstationary signal using a combination of fractional spectrograms (FS). A high resolution time frequency distribution (TFD) is defined by combining FS computed using windows of varying lengths and chirp rates. The IF of individual signal components is then computed by applying a peak detection and component extraction procedure. The mean square error (MSE) of IF estimates computed with the AFS is lower than the MSE of IF estimates obtained from other TFDs for SNR varying from -5 dB to 16 dB.