# Homework Help: Coherent versus incoherent averaging of data

1. May 22, 2010

### EightBall

I'm doing an assignment for the course Earth Observation. one of the questions is to plot an image in Matlab. you are given 5 data files containing each a 2400x2000 matrix with complex values at each matrix element. these 5 data files can be transformed into 5 images since each data file is in fact an image of the same place on earth taken at a different time. the goal now is to combine these 5 images into 1 image by the means of averaging. this has to be done on two ways: coherent averaging and incoherent averaging. in the assignment is explained how you should do the averaging, but what the assignment does not tell is what it exactly does to your data and why it is done that way. now I've applied the two averaging methods and i get 2 images. the one made with coherent averaging does not look different from the 5 images that were combined. The image obtained through incoherent averaging however does look a lot sharper (less speckles). now the question of the assignment is not only what is the difference, but also why is there a difference? this is also the question i want to ask you. Because i don't understand what the difference is between coherent and incoherent averaging or what it does and why it does what it does, i can't answer the question of the assignment

what the assignment says about coherent and incoherent averaging is the following:
'For coherent averaging, the real and the imaginary parts of the radar signals are summed
separately, and later combined into complex numbers, resulting in a coherent average.
For the incoherent average, only the absolute values of the complex data are summed,
disregarding the phase information.'

I've tried to search the internet about these averaging methods. I only found out that incoherent averaging 'destroys' in some way the phase information of the data. but this didn't made me any wiser.