Abstract: Methods of denoising a neural recording signal include correlating a neural recording signal with a number of basis functions to obtain a number of weights and then multiplying the weights with the basis functions to obtain a denoised neural recording signal. The basis functions are derived using principal component analysis. Systems for denoising a neural recording signal include one or more devices configured to correlate a neural recording signal with the basis functions to obtain the weights and then multiply the weights with the basis functions to obtain the denoised neural recording signal.