How to make blur image?

Original image:


And when scroll it, I need blur effect like:

How to make this?

 

Normally blur is done by sampling the texture several times in a shader. You could write your own shader that instead of taking one sample, take 5 samples in the same row (because you only need directional blurring).

Or in an easier way, you could duplicate the text several times with a horizontal displacement and assign different alphas to each Text. The alphas should be higher on the center and fade out on the texts near the border.

That should mimic the same result, the more times you duplicate your text, the more smooth will be the result but the perfomance will be lower.