Physically meaningful amplitude of exponential function following convolution?

As an example, I am calculating the discrete convolution of an exponentially decaying function ExpDec with a measured instrument response function IRF (both sampled at intervals timeStep):

Conv = real(ifft(fft(IRF).*fft(ExpDec)))*timeStep;

The amplitude of the obtained convolution function Conv makes sense mathematically, but physically does not tell me much about the amplitude of the underlying decay function ExpDec. I tried to account for this by dividing Conv by a reference value (at a time at which ExpDec is to a good aproximation not affected by the IRF), but I was wondering if there a better way of doing this to extract a physically meaninful amplitude?