I have measured an exponential decay which is distorted by detection system. I measured the transfer function of the detection system in frequency domain. I performed convolution between real true exponential and transfer function and fit it with experimental data. I get good agreement for lower time constant but for high time constant, it is not working. What would be the possible regions? (I only measure the amplitude as a function of frequency for the transfer function. I write a complex function with some parameters and fit it's absolute value with experimental transfer function to get the complex transfer function back.)