中文摘要：

最小能量（小波）框架在信号处理领域有着广泛的应用前景,但目前只能应用在连续信号上.为解决这一问题,给出了离散信号空间上的最小能量框架的定义,并证明了它所具备的一些优良性质.在实际应用中,针对通信领域中的受加性高斯白噪声污染的二进制矩形脉冲信号提出一个新的去噪算法,利用离散空间上一个最小能量框架对接收波形的抽样离散数列进行去噪工作,获得了较好的处理效果.仿真结果表明,如果利用该算法对接收波形进行去噪预处理,则接收机可以降低误码率,在信噪比4dB处获得了3.4dB的性能增益.

英文摘要：

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 denoising 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.