Apparatus and method for generating a sound field

A method for generating a sound field on the basis of an input audio signal, wherein the method comprises the steps of:

• providing or receiving a first transducer driving signal vector q0 of dimension L such that a gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), wherein J(q;ψ) is a cost function having as variables a transducer driving signal vector q of dimension L and a weight matrix ψ of dimension M×M, and wherein ψ0 is a first weight matrix of dimension M×M;
• providing a second transducer driving signal vector {tilde over (q)} of dimension L such that a gradient of the cost function J(q;ψ) with respect to q is zero in ({tilde over (q)};
• {tilde over (ψ)}), wherein {tilde over (ψ)} is a second weight matrix of dimension M×M, and wherein the second transducer driving signal vector {tilde over (q)} is provided on the basis of:
• the first transducer driving signal vector q0,
• the first weight matrix ψ0, and
• the second weight matrix {tilde over (ψ)};
• and
• driving each transducer of a plurality of L transducers by a respective component {tilde over (q)}l, l∈{1, . . . , L}, of the second transducer driving signal vector {tilde over (q)};
• wherein the cost function is J(q;ψ)=∥{tilde over (ψ)}(p−p)∥2+β∥q∥2, wherein p is a target pressure vector of dimension M comprising M target pressure values pm for a set of M control points, m∈{1, . . . , M}, p is a pressure vector of dimension M comprising M pressure values pm for the set of M control points, m∈{1, . . . , M}, and β is a regularization parameter in the range of [0,∞).

A non-transitory storage medium carrying a program code which when executed by one or more processors of a computer causes the computer to perform a method of generating a sound field on the basis of an input audio signal, wherein the method comprises the steps of:

• providing or receiving a first transducer driving signal vector q0 of dimension L such that a gradient of J(q;ψ) with respect to q is zero in (q0;ψ0), wherein J(q;ψ) is a cost function having as variables a transducer driving signal vector q of dimension L and a weight matrix ψ of dimension M×M, and wherein ψ0 is a first weight matrix of dimension M×M;
• providing a second transducer driving signal vector {tilde over (q)} of dimension L such that a gradient of the cost function J(q;ψ) with respect to q is zero in ({tilde over (q)};
• {tilde over (ψ)}), wherein {tilde over (ψ)} is a second weight matrix of dimension M×M, and wherein the second transducer driving signal vector {tilde over (q)} is provided on the basis of:
• the first transducer driving signal vector q0,
• the first weight matrix ψ0, and
• the second weight matrix {tilde over (ψ)};
• and
• driving each transducer of a plurality of L transducers by a respective component {tilde over (q)}l, l∈{1, . . . , L}, of the second transducer driving signal vector {tilde over (q)};
• wherein the cost function is J(q;ψ)=∥{tilde over (ψ)}(p−p)∥2+β∥q∥2, wherein p is a target pressure vector of dimension M comprising M target pressure values pm for a set of M control points, m∈{1, . . . , M}, p is a pressure vector of dimension M comprising M pressure values Pm for the set of M control points, m∈{1, . . . , M}, and β is a regularization parameter in the range of [0,∞).