Let us assume we had time domain signal as a raw data R (Window 1) and we wish to perform the deconvolution process on R using another set of raw data G (window 2). This is accomplished dividing FT of R by the FT of G. However, after inverse FT, the noise in the data has noise as shown in the bottom window. This is just a simulation of Fourier deconvolution , however in real case, after an inverse FT, signal to noise is very low.
I have seen apodization with triangular windows in the time domain, which is very simple before the data is Fourier transformed. The raw signal is multiplied by a triangular window before performing FT by using the following function, where N is the total number of points, and n is the nth data point.
The key question is can we perform apodization i.e., apply a triangular window on complex discrete obtained after FT to cut off high frequency noise in the Fourier domain after performing deconvolution? Thanks.