Electronics Computers

Digital applications have developed rapidly over the last few decades. Since many sources of information are of analog or continuous-time nature, discrete-time signal processing (DSP) inherently relies on sampling a continuous-time signal to obtain a discrete-time representation. Consequently, sampling theories lie at the heart of signal processing applications and communication systems. A few examples are sampling rate conversion between audio formats and for software radio [1], biomedical imaging [2], lens distortion correction, super-resolution of image sequences and more. To accommodate high operating rates while retaining low computational cost, efficient analog-to-digital (ADC) and digital-to-analog (DAC) converters must be developed. Many of the limitations encountered in current con-verters is due to a traditional assumption that the sampling stage must acquire the data at the Shannon-Nyquist rate, corresponding to twice the signal bandwidth [3], [4], [5]. To avoid aliasing, a sharp low-pass filter must be implemented prior to sampling. The reconstructed signal is also a bandlimited function, generated by integer shifts of the sinc interpolation kernel. A major drawback of this paradigm is that many natural signals are better represented in alternative bases other than the Fourier basis [6], [7], [8], or possess further structure in the Fourier domain. In addition, ideal point-wise sampling, as assumed by the Shannon theorem, cannot be implemented. More practical ADCs introduce a distortio