Present disclosure describes an improved scaling mechanism for a multi-stage fixed-point FFT algorithm used to process signals received by radar or sonar systems. Proposed scaling includes scaling an output of every pair of consecutive butterfly stages of the FFT algorithm by a scaling factor equal to two times of the inverse of a growth factor for the pair of consecutive butterfly stages for the FFT algorithm for a purely complex exponential input signal. Besides this scaling, input signals are allowed to overflow by saturation. Such mechanism yields adequate performance of radar and sonar receivers implementing fixed-point FFTs for any types of input signals, from random to substantially complex exponential or sinusoidal signals. Proposed scaling achieves a balance between having signal to noise ratio (SNR) that is possible to obtain for a particular input signal and SNR that is needed to successfully process that signal for radar and sonar applications.