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Sampling theories lie at the heart of signal processing devices andcommunication systems. To accommodate high operating rates while retaining lowcomputational cost, efficient analog-to digital (ADC) converters must bedeveloped. Many of limitations encountered in current converters are due to atraditional assumption that the sampling state needs to acquire the data at theNyquist rate, corresponding to twice the signal bandwidth. In this thesis amethod of sampling far below the Nyquist rate for sparse spectrum multibandsignals is investigated. The method is called periodic non-uniform sampling,and it is useful in a variety of applications such as data converters, sensorarray imaging and image compression. Firstly, a model for the sampling systemin the frequency domain is prepared. It relates the Fourier transform ofobserved compressed samples with the unknown spectrum of the signal. Next, thereconstruction process based on the topic of compressed sensing is provided. Weshow that the sampling parameters play an important role on the average sampleratio and the quality of the reconstructed signal. The concept of conditionnumber and its effect on the reconstructed signal in the presence of noise isintroduced, and a feasible approach for choosing a sample pattern with a lowcondition number is given. We distinguish between the cases of known spectrumand unknown spectrum signals respectively. One of the model parameters isdetermined by the signal band locations that in case of unknown spectrumsignals should be estimated from sampled data. Therefore, we applied bothsubspace methods and non-linear least square methods for estimation of thisparameter. We also used the information theoretic criteria (Akaike and MDL) andthe exponential fitting test techniques for model order selection in this case.

Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio