<p>Signal processing in memristive neurons is fundamental to both neuromorphic computing and biological information processing. Such systems inherently exhibit time delay and stochastic fluctuations, among other complexities. Nevertheless, how noise-coupled time delay impacts signal processing remains unexplored in memristive neurons. Here, we numerically investigate the dynamics and response of a memristive neuron model subjected to noise and time delay. Without noise, increased time delay leads to a transition of neuronal firing from chaotic to periodic patterns, demonstrated by Lyapunov exponents and interspike interval analysis. Stochastic resonance occurs in noisy systems, enhancing signal processing at optimal noise levels. The spectral response analysis reveals distinct stochastic resonance at a short time delay and medium noise intensity, while stochastic anti-resonance emerges at a long time delay and weak noise intensity. We systematically identify optimal combinations of delay and noise parameters to maximize neuronal response and signal processing. These results highlight the combined influence of time delay and noise on neuronal excitability, providing theoretical guidance for designing robust neuromorphic systems optimized for weak-signal processing in noisy environments.</p>