In this paper, a neural network approach is introduced to estimate non-noisy speed and torque from noisy measured currents and voltages in induction motors with Variable Speed Drives. The proposed estimation method is comprised of a neural speed-torque estimator and a neural signal denoiser. A new training strategy is introduced that combines large amount of simulated data and a small amount of real world data. The proposed denoiser does not require non-noisy ground truth data for training, and instead uses classification labels which are easily generated from real-world data. This approach improves upon existing noise removal techniques by learning to denoise as well as classify noisy signals into static and dynamic parts. The proposed neural network based denoiser generates clean estimates of currents and voltages which are then used as inputs to the neural network estimator of speed and torque. Extensive experiments show that the proposed joint denoising-estimation strategy performs very well on real data benchmarks. The proposed denoising method is shown to outperform several widely used denoising methods and a proper ablation study of the proposed method is conducted.