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I am not sure if this is the correct forum, but...

I am working with FFTs of real signals. I have a FFT of a time signal (call it R(f)) and a frequency response (output/input) function (call it H(f)).

The math is simple, I want to know what I need to put into my system defined by H(f) to get R(f) out. This is simple division:

input(t) = IFFT[R(f) ./ H(f)]

The problem arises because the IFFT often returns signals that do not begin/end at 0 - so when I apply the signal to my physical plant, there is a transient created by the instant jump from 0 to input(t=0). The FFT assumes a continuous repetition of my input(t) signal, which is why it is OK for it to output a non-zero-initial signal as it starts and ends at the same non-zero value.

From my basic analysis, I have found that Real(sum([R(f) ./ H(f)])) must be zero.

Any ideas on how to force the IFFT of the signal to be zero?