158 2. Wiener Filtering 159 3. Speech Enhancement by Short-Time Spectral Modification 3. 1 Short-Time Fourier Analysis and Synthesis 159 160 3. 2 Short-Time Wiener Filter 161 3. 3 Power Subtraction 3. 4 Magnitude Subtraction 162 3. 5 Parametric Wiener Filtering 163 164 3. 6 Review and Discussion Averaging Techniques for Envelope Estimation 169 4. 169 4. 1 Moving Average 170 4. 2 Single-Pole Recursion 170 4. 3 Two-Sided Single-Pole Recursion 4. 4 Nonlinear Data Processing 171 5. Example Implementation 172 5. 1 Subband Filter Bank Architecture 172 173 5. 2 A-Posteriori-SNR Voice Activity Detector 5. 3 Example 175 6. Conclusion 175 Part IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. Introduction 181 2. Differential Microphone Arrays 182 3. Array Directional Gain 192 4. Optimal Arrays for Spherically Isotropic Fields 193 4. 1 Maximum Gain for Omnidirectional Microphones 193 4. 2 Maximum Directivity Index for Differential Microphones 195 4. 3 Maximimum Front-to-Back Ratio 197 4. 4 Minimum Peak Directional Response 200 4. 5 Beamwidth 201 5. Design Examples 201 5. 1 First-Order Designs 202 5. 2 Second-Order Designs 207 5. 3 Third-Order Designs 216 5. 4 Higher-Order designs 221 6. Optimal Arrays for Cylindrically Isotropic Fields 222 6. 1 Maximum Gain for Omnidirectional Microphones 222 6. 2 Optimal Weights for Maximum Directional Gain 224 6. 3 Solution for Optimal Weights for Maximum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.

158 2. Wiener Filtering 159 3. Speech Enhancement by Short-Time Spectral Modification 3. 1 Short-Time Fourier Analysis and Synthesis 159 160 3. 2 Short-Time Wiener Filter 161 3. 3 Power Subtraction 3. 4 Magnitude Subtraction 162 3. 5 Parametric Wiener Filtering 163 164 3. 6 Review and Discussion Averaging Techniques for Envelope Estimation 169 4. 169 4. 1 Moving Average 170 4. 2 Single-Pole Recursion 170 4. 3 Two-Sided Single-Pole Recursion 4. 4 Nonlinear Data Processing 171 5. Example Implementation 172 5. 1 Subband Filter Bank Architecture 172 173 5. 2 A-Posteriori-SNR Voice Activity Detector 5. 3 Example 175 6. Conclusion 175 Part IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. Introduction 181 2. Differential Microphone Arrays 182 3. Array Directional Gain 192 4. Optimal Arrays for Spherically Isotropic Fields 193 4. 1 Maximum Gain for Omnidirectional Microphones 193 4. 2 Maximum Directivity Index for Differential Microphones 195 4. 3 Maximimum Front-to-Back Ratio 197 4. 4 Minimum Peak Directional Response 200 4. 5 Beamwidth 201 5. Design Examples 201 5. 1 First-Order Designs 202 5. 2 Second-Order Designs 207 5. 3 Third-Order Designs 216 5. 4 Higher-Order designs 221 6. Optimal Arrays for Cylindrically Isotropic Fields 222 6. 1 Maximum Gain for Omnidirectional Microphones 222 6. 2 Optimal Weights for Maximum Directional Gain 224 6. 3 Solution for Optimal Weights for Maximum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.

158 2. Wiener Filtering 159 3. Speech Enhancement by Short-Time Spectral Modification 3. 1 Short-Time Fourier Analysis and Synthesis 159 160 3. 2 Short-Time Wiener Filter 161 3. 3 Power Subtraction 3. 4 Magnitude Subtraction 162 3. 5 Parametric Wiener Filtering 163 164 3. 6 Review and Discussion Averaging Techniques for Envelope Estimation 169 4. 169 4. 1 Moving Average 170 4. 2 Single-Pole Recursion 170 4. 3 Two-Sided Single-Pole Recursion 4. 4 Nonlinear Data Processing 171 5. Example Implementation 172 5. 1 Subband Filter Bank Architecture 172 173 5. 2 A-Posteriori-SNR Voice Activity Detector 5. 3 Example 175 6. Conclusion 175 Part IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. Introduction 181 2. Differential Microphone Arrays 182 3. Array Directional Gain 192 4. Optimal Arrays for Spherically Isotropic Fields 193 4. 1 Maximum Gain for Omnidirectional Microphones 193 4. 2 Maximum Directivity Index for Differential Microphones 195 4. 3 Maximimum Front-to-Back Ratio 197 4. 4 Minimum Peak Directional Response 200 4. 5 Beamwidth 201 5. Design Examples 201 5. 1 First-Order Designs 202 5. 2 Second-Order Designs 207 5. 3 Third-Order Designs 216 5. 4 Higher-Order designs 221 6. Optimal Arrays for Cylindrically Isotropic Fields 222 6. 1 Maximum Gain for Omnidirectional Microphones 222 6. 2 Optimal Weights for Maximum Directional Gain 224 6. 3 Solution for Optimal Weights for Maximum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.