A scaling approach for FFT processing

In signal processing, multidimensional FFTs and circular convolution filters implemented via multiplication in the frequency domain are used frequently. To avoid amplitude modulation of the signal, a scaling based upon criteria involving multiple FFTs must be employed; a direct application of block floating point is inadequate. A scaling approach is described that is based upon the cumulative distribution function of the quantized signal. The characteristics of the cumulative distribution function are used in estimating the position of the standard deviation of the signal plus noise in the quantization aperture.