Convolutional Neural Networks (CNNs) for audio processing typically learn discrete, fixed grid representations, making them brittle across varying sample rates. We present a 1D Fourier Neural Operator (FNO) designed for continuous scale invariant audio denoising. By formulating the signal as a continuous function in the frequency domain and utilizing a curriculum fine tuning approach with alternating multi rate batches, we achieve state of the art zero shot generalization. Evaluated on 44.1 kHz audio, our model achieves a Scale Invariant Signal to Distortion Ratio (SI-SDR) of 14.51 dB outperforming the 16 kHz trained Wave-U-Net baseline (12.74 dB) without requiring full retraining. Ablation studies yield a potential architectural simplification: multi rate fine tuning curricula rather than explicit coordinate mapping are the primary drivers of scale invariance. This finding allows for a simpler architecture that maintains O (N log N) efficiency while offering a robust, resolution agnostic pathway for audio processing.