A Modeling Problem of a Continuous-Time Domain Signal and Its Discrete Counterpart

In this paper, a new class of continuous in the time domain signals is proposed. Its equivalent discrete versions are also considered. The paper presents the necessary analytical formulae to prove the desired properties of the continuous spectrum as well as the discrete spectrum. These signals are practically pass-band restricted up to the level of relevance equals −120 dB. The proposed signals can be used to test any passband system such as radar, telecommunication, and others. In particular, these signals are suitable for testing hybrid systems where continuous and discrete-time domains are mixed. The signals proposed here fill tightly the entire usable bandwidth of a hybrid system. That means no frequency bins are omitted during the design and testing. This is an important feature for the accuracy of computer simulations. Good accuracy of computer simulations gives a strong promise for a hardware implementation of such a system, suitable for engineering applications. The authors also suggest the use of a few percent guard bands at both ends of the useful band. Therefore, the effect of the guard bands on the quality of the continuous spectrum representation into finite computer memory is also deliberated.