Speech super-resolution (SSR) aims to predict a high resolution (HR) speech signal from its low resolution (LR) corresponding part. Most neural SSR models focus on producing the final result in a noise-free environment by recovering the spectrogram of high-frequency part of the signal and concatenating it with the original low-frequency part. Although these methods achieve high accuracy, they become less effective when facing the real-world scenario, where unavoidable noise is present. To address this problem, we propose a Super Denoise Net (SDNet), a neural network for a joint task of super-resolution and noise reduction from a low sampling rate signal. To that end, we design gated convolution and lattice convolution blocks to enhance the repair capability and capture information in the time-frequency axis, respectively. The experiments show our method outperforms baseline speech denoising and SSR models on DNS 2020 no-reverb test set with higher objective and subjective scores.