Bilgi dağılımının yayılan sinyallerin geri çatılması üstündeki etkisi

Interpolation is one of the fundamental concepts in signal processing. The analysis of the di culty of interpolation of propagating waves is the subject of this thesis. It is known that the information contained in a propagating wave eld can be fully described by its uniform samples taken on a planar surface transversal to the propagation direction, so the eld can be found anywhere in space by using the wave propagation equations. However in some cases, the sample locations may be irregular and/or nonuniform. We are concerned with interpolation from such samples. To be able to reduce the problem to a pure mathematical form, the fractional Fourier transform is used thanks to the direct analogy between wave propagation and fractional Fourier transformation. The linear relationship between each sample and the unknown eld distribution is established this way. These relationships, which constitute a signal recovery problem based on multiple partial fractional Fourier transform information, are analyzed. Recoverability of the eld is examined by comparing the condition numbers of the constructed matrices corresponding to di erent distributions of the available samples.