Advances in audio data compression are largely driven by the need to conserve transmission rate or bandwidth, while maintaining the ability to accurately reconstruct the signal at the receiver. This report examines data compression methods with an emphasis on techniques for the compression of audio data. An overview of data compression schemes is presented to provide the background for a performance comparison between selected versions of data compression systems featuring adaptive differential pulse code modulation (ADPCM) schemes. Two different types of data compression systems are investigated; IIR and FIR impulse implementations. A modification to the basic ADPCM system using a modular function is implemented. The modular operation results in a smaller size codebook and prevents data expansion when the source is not matched to the code. This modification is utilized for both types of ADPCM coders compared. To complete the compression system Huffman coding, is employed to encode and decode the compressed data to and from binary form.