||Bandwidth extension (BWE) is a field that has attracted increasing attention in recent years because bandwidth reduction can happen, for example, during recording, transmission (including storage), or reproduction. One way to extend the bandwidth of output is changing the transmission systems physically, which is hard to implement in practice due to economical and historical reasons. Another traditional method is to derive the missing frequency components only from the available bandwidth-limited signal, without referring to the transmission process. This thesis is concerned with a new BWE algorithm based on the transfer function of multiple deterministic systems, using the tools of Fourier transform. The traditional definition of transfer function in linear time-invariant systems is extended further into nonlinear systems, and the basic hardware requirement is the availability of changing the digital energy to the actual force. Experiments and simulations of low-pass filter system, audio system, or imaging system are operated to explore the bandwidth extension properties of this algorithm. In general, it is discovered and proved that this BWE method is effective to recover high-band output signal for different systems, assessed by various evaluation terms.