# How to append two bandlimited signals and make the result bandlimited without modifying the first signal

I need to append (not add) a bandlimited signal F(b) to a bandlimited signal F(a) and keep the result bandlimited without modifying the part that corresponds to F(a).

Both are bandlimited to the same frequency (for example to 1/4 the Nyquist frequency). If F(a) is 100 samples long and F(b) is 100 samples long, the result F(c) is 200 samples in length and the first 100 samples of F(c) are identical to F(a).

An obvious "solution" is to filter the boundary so that the discontinuity can be made bandlimited, but in this case, I am restricted from modifying the samples in F(a).

How can I filter (or manipulate) F(b) such that the result of appending the two signals is also bandlimited to the same frequency and preserves the integrity of F(b) as much as possible?

Edit: For context, here's the problem I'm trying to solve. I am performing procedural terrain generation using 2D heightmaps and need to add a tile of terrain to a pre-existing landscape that may or may not have been procedurally generated. I'm looking for an algorithm that will "smooth" the borders of the tiles so that the tile boundaries are not noticeable.

• It is not clear what you mean. Bandlimited signal is infinite in time domain. See for example - en.wikipedia.org/wiki/… Oct 7, 2013 at 7:37
• Hi SergV - I mean bandlimited in the practical rather than the theoretical sense. In other words, the signals can be thought of as sampled signals that have been passed through a low-pass filter.
– Ting
Oct 7, 2013 at 17:57
• I think it's better if you explain what problem you want to solve. If you work with music signals then answer of Hilmar is OK. About theory and practice. Theory say that bandlimited signal is infinite in time and you have a big problem in practice when trying to merge 2 such signals. Oct 8, 2013 at 2:33
• Thanks for the feedback. I've edited the question to provide more context.
– Ting
Oct 9, 2013 at 4:11