Laplace-transform and Z-transform theories have been applied to analyze the tensile stress-strain curves of a co-woven-knitted (CWK) composite under quasi-static (0.001/s) and high strain rates (up to 2586/s) tension. The transform results were extended to characterize the tension failure and dynamic responses of the CWK composite in the frequency domain. Specifically, the Laplace-transform theory was employed to analyze the stress-strain curves of the CWK composite along 0 , 45 and 90 directions when the composite is assumed to be a continuous system, while the Z-transform theory was used for the discrete system for the composite. From the transformed results, it was found that the stress-strain curves of the CWK composite specimen under different strain rates tension have similar stability behaviours for the Laplace-and Z-transform. For the continuous system, few pole plots are distributed on the left side of the imaginary axis, which means the system is unstable. Nevertheless, the pole-plot distribution is stable before the post-critical deformation of the CWK composite. For the discrete system, most of the poles are located inside the unit circle before post-critical deformation, indicating the system is stable. From the stiffness-time history and fracture morphology, the stability of the pole-plot distribution corresponds to the stiffness stability and fracture uniformity. From continuous and discrete system analyses, it is found that the stress-time and strain-time histories of the CWK composite can be regarded as a digital signal system. Digital signal processing (DSP) methods can be extended to the investigation of the mechanical behaviour of composites.