Steganography is considered one of the widely used methods for hiding information; it hides secret data in
digital cover without clear suspicion. This work focus on studying two methods for hiding any secret data type in the audio signal. First, the audio signal is transformed to frequency domain by using quick Fourier transform that depended on the reduction of time and number of mathematical operations. Two hiding methods are designed to embed secret data bits in the phase domain coefficients of audio signal. The first method, called hiding in voiced blocks (HVB), implies the inserting of secret bits in the voiced parts of audio data. While the second method, called hiding in checked blocks (HCB), implies the insertion of secret bits in audio blocks that successfully passed the integrity retrieved bits tests. These two methods use two types of wave audio cover files channels (mono and stereo). Finally, the performance of the proposed hiding methods was tested by using fidelity measures mean square error (MSE), signal noise ratio (SNR), and peak signal noise ratio (PSNR) to measure the rate of error, and the hiding rate was computed to assess the embedding power of each hiding method. Also, the effects of some control parameters on the system performance were investigated to assist user to correctly choose the values of system parameters. The test results indicate that the HVB method shows more embedding power than HCB method, but not all the embedded secret bits could correctly retrieved when HVB method is utilized.