Adaptive filter with two inputs I have general theoretical questions: 


Is it true that an adaptive filter with two inputs (one normal and one delayed by the single time increment) can completely get rid of any single frequency noise? 
Is it then true that a three-input adaptive filter can (completely) get rid of a noise consisting of two harmonics, etc.? 


Maybe there is a theorem for this, any pointers would be appreciated.
I've had a look at the problem in the book you've cited (Figure 10.7, Adaptive Filter for Noise Cancellation).  As Dan has stated, a linear combination can filter out a specific frequency, but it depends on the specific noise frequency, the sample rate, and the length of the adaptive filter delay-line (i.e. the number taps or weights used in the adaptive filter).

In general, however, a given adaptive filter arrangement used for noise cancellation (i.e. sample rate, length of delay-line, adaptive algorithm) will dictate what specific frequencies of the noise will be attenuated.