The minimum-energy (wavelet) frame has an extensive application prospect in the field of signal processing, but now it can be applied only to continuous signals. In order to solve the problem, we define a minimum-energy frame in the discrete signal space, and then prove that it has some good properties. In the actual application, we propose a new de-noising algorithm which is special for the binary rectangular pulse signal polluted by the additive gaussian noise and obtain better processing effect by using a minimum-energy frame in the discrete signal space to denoise the sampled sequence of receiving waveform. The simulation results show that if a pre-processing link is used to denoise the receiving waveform through using the algorithm, the receiver can reduce the bit error rate and achieve a 3.4 dB performance gain at 4 dB signal-to-noise ratio.