Table 2 Algorithm for estimating the embedding rate

Input: A blended speech signal X of length N

Output: Hidden location of the secret speech and the estimated embedding rate

Step 1: For a given speech signal X, invert its odd–even points to obtain the inverted version \(X_{w}\)

Step 2: Calculate the OED of X, which is denoted by \(D_{r}\), and the OED of \(X_{w}\), which is denoted by \(D_{w}\)

Step 3: Calculate the average ZCRs of \(D_{r}\) and \(D_{w}\), respectively, which are denoted by \(Z(D_{r} )\) and \(Z(D_{w} )\), and set \(Q_{mean} = \hbox{min} (Z(D_{r} ),Z(D_{w} ))\)

Step 4: If \(Z(D_{r} ) \le Z(D_{w} )\), set \(D = D_{r}\); otherwise, \(D = D_{w}\)

Step 5: Divide D into N frames and calculate the average ZCR per frame, which is denoted by \(Q(i)\), where i denotes the ith frame

Step 6: Let \(Flag(i)\) denote the symbol of the ith frame: \(Flag(i) \in \{ 0,1\}\). If \(Q(i) < Q_{mean}\), set \(Flag(i) = 0\); otherwise, \(Flag(i) = 1\)

Step 7: The hang-over scheme (Avcıbas 2006; Muhammad 2015), which is a type of VAD algorithm, is used for \(Flag(i)\) to mark the secret speech segments, thereby ensuring that the hidden location of the secret speech is determined

Step 8: Calculate the length of the secret speech segments and the embedding rate