T. Cooklev has published over 20 journal papers and over 30 conference papers in the areas of digital signal processing, audio and video compression, fast algorithms, and wireless communications. For one of his papers he received the Best Paper Award at the 1994 IEEE Asia-Pacific Conference on Circuits and Systems, Taipei, Taiwan. He is the inventor on 5 issued and about 12 pending patents in the United States.
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I know this doesn’t address your problem directly but typical technique is to divide into 2^n samples chunks and process; possibly with overlapping blocks, possibly applying a window function (Google it) depending on desired frequency response. If you are modifying the FFT and applying an inverse you will want overlapping blocks, cross-faded in output, because you will get audible clicks between blocks if the apparent phase (or the 0Hz constant term) changes. BTW, frequency (Hz) is index * sample_rate / block_size
Source: fft mp3 chunks – Google Search