Neural fields, also known as coordinate-based representations, are an emerging signal representation framework. This approach has also been used to represent audio signals, but the generated audio often contains noise. To reduce noise and improve representation quality, we propose using waveform encoding in the neural field. Instead of yielding real numbers for each temporal coordinate, this involves using discrete integers as outputs with waveform-encoded integers as target classes, and treating the representation problem as a classification task rather than a regression problem. The experimental results show that waveform encoding can improve the audio quality of neural fields across a variety of audio datasets.