Motivated by environmental concern, the industry has been developing an alternative marine seismic source, in particular a marine vibrator. By spreading the emitted energy out over time, vibrator sources are perceived to be less intrusive to marine mammals. It is also believed that vibrators have greater control of the emitted source wavelet than can be achieved with traditional airguns. With the added control, it is possible to only emit portions of the frequency spectrum, which in turn allows for many applications such as deblending and the ability to avoid masking mammal communications. To effectively implement these, two methodologies are proposed to interpolate the frequency data that are not emitted. The first is a deep learning approach utilizing a U-Net architecture, with a custom frequency loss function. The second is a sparse optimization method that approximates the reflectivity series of the subsurface using known frequency content. By assuming that the signal can be represented sparsely and that all frequencies interact with the subsurface interfaces similarly at all frequencies, the frequency spectrum can be reconstructed. Both of the presented methods are tasked to interpolate the missing frequency band(s) in North Sea shot data. It is found that both methods are able to interpolate narrow 2.5 Hz bands, but are unable to accurately reconstruct wider (ex. 10 Hz), frequency bands. Overall, the U-Net shows better results than the sparse optimization method when the frequency gaps are positioned closely.