The echo signal simulation of Synthetic Aperture Radar (SAR) is the basis of the research on SAR signal processing, and the large computation cost is the primary shortcomings of the frequently-used echo signal simulation method. Using the theory that Stolt transformation can simulate the so-called space-varying property of range migration, the IωKA algorithm becomes an impressive fast echo signal simulation method for the extended scenes in the two-dimensional frequency domain, and the computational cost and operation time is cut down sharply. According to the analysis, the key to the IωKA algorithm is the interpolation for the Stolt transformation, and the signal before interpolation in the IωKA algorithm can be seen as a band-limited signal in the strict sense, which is greatly different from that in the ωKA algorithm and may has a great effect on the selection of the interpolation algorithm and the interpolation performance. By preprocessing, the signal before interpolation in the IωKA algorithm is transformed into a baseband band-limited signal in the strict sense, which improves the interpolation performance, reduces the complexity of the interpolation, and enlarges the application range of the algorithm. Experimental result shows that if the error introduced by the simulation is regarded as noise, the error level of our method is much less than the system noise. Also, Compared with the other 2-D frequency-domain simulation methods, this method has a small amplitude error and phase error, and could be applied to the whole strip mode SAR with varieties of squint angles and wide-beam.