Automatic speech recognition (ASR) systems are vulnerable to audio adversarial examples, which aim at deceiving ASR systems by adding perturbations to benign speech signals. These audio adversarial examples appear indistinguishable from benign audio waves, but the ASR system decodes them as intentional malicious commands. Previous studies have demonstrated the feasibility of such attacks in simulated environments (over-line) and have further showcased the creation of robust physical audio adversarial examples (over-air). Various defense techniques have been proposed to counter these attacks. However, most of them have either failed to handle various types of attacks effectively or have resulted in significant time overhead. In this article, we propose a novel method for detecting audio adversarial examples. Our approach involves feeding both smoothed audio and original audio inputs into the ASR system. Subsequently, we introduce noise to the logits before providing them to the decoder of the ASR. We demonstrate that carefully selected noise can considerably influence the transcription results of audio adversarial examples while having minimal impact on the transcription of benign audio waves. Leveraging this characteristic, we detect audio adversarial examples by comparing the altered transcription, resulting from logit noising, with the original transcription. The proposed method can be easily applied to ASR systems without requiring any structural modifications or additional training. Experimental results indicate that the proposed method exhibits robustness against both over-line and over-air audio adversarial examples, outperforming state-of-the-art detection methods.