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Interpolation of discrete periodic nonuniform decimation using alias unraveling

We consider the problem of signal restoration when P of every N samples in a discrete time system are uniformly decimated. The degraded signal is an aliased form of the original signal. The aliasing can, in certain cases, be unraveled by application of multiplicative discrete time trigonometric polynomials followed by filtering. The filter output is the restored discrete time signal. Conditions required for this restoration are presented. The condition - and thus the noise sensitivity - of the restoration process is also analyzed.