This research proposes a new signal representation based an multiscale zero-crossings of the signal. It is shown that the original signal is uniquely characterized by its zero-crossing representation. The representation is insensitive to translation of the input signal. In this approach, the zero-crossing information is supplemented with the first moment of the signal to stabilize the representation. This technique, initially suggested by others for wavelet transform zero-crossings, results in a method for reconstructing the original signal from its multiscale zero-crossings. The signal recovery algorithm is fast and efficient, and suggests completeness of the representation. The representation has been successfully applied to the classification of ultrasonic nondestructive evaluation signals from of welds, multiresolution reconstruction of images and unsupervised signal denoising.