In order to have a good separation of the subject from the background you usually use fast lens with high aperture and so on.
Can this, however, be achieved purely digitally?
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Many options exist for creating bokeh digitally. Some purists will tell you that nothing exists like true bokeh created from large apertures. But, if you want to experiment many options are available.
If you want to create it yourself in something like Photoshop or Gimp, you can using the Gaussian Blur filter effect. I will caution you though, this is a "pet-peeve" of many photographers, much like selective coloring. If you use this effect too much or too obviously to the viewer - it can have a negative effect on your image, so take caution.
Note, fast lenses with large apertures have other benefits besides the pleasing bokeh they produce. In my opinion the "synthetic" options do not match the real thing for bokeh either.
For truly imitating bokeh, you'd have to adjust blur of each background pixel based on how much away from focus plane it is along the depth axis. Since your image does not contain that information, it's quite hard to fake bokeh purely by post-processing unless it's all at similar distance, in which case you could use Gaussian blur and layer masking.
You might, however, try achieving better bokeh by stitching multiple exposures.