  We present exact results for the transmission coefficient of a linear lattice
at one or more sites of which we attach a Fibonacci quasiperiodic chain. Two
cases have been discussed, viz, when a single quasiperiodic chain is coupled to
a site of the host lattice and, when more than one dangling chains are grafted
periodically along the backbone. Our interest is to observe the effect of
increasing the size of the attached quasiperiodic chain on the transmission
profile of the model wire. We find clear signature that, with a side coupled
semi-infinite Fibonacci chain, the Cantor set structure of its energy spectrum
should generate interesting multifractal character in the transmission spectrum
of the host lattice. This gives us an opportunity to control the conductance of
such systems and to devise novel switching mechanism that can act over
arbitrarily small scales of energy. The Fano profiles in resonance are observed
at various intervals of energy as well. Moreover, an increase in the number of
such dangling chains may lead to the design of a kind of spin filters. This
aspect is discussed.
