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Real-Time Digital Signal Processing : Fundamentals, Implementations and Applications.

By: Material type: TextTextSeries: New York Academy of Sciences SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2013Copyright date: ©2013Edition: 1st edDescription: 1 online resource (566 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118706695
Subject(s): Genre/Form: Additional physical formats: Print version:: Real-Time Digital Signal ProcessingDDC classification:
  • 621.382/2
LOC classification:
  • TK5102.9 .K86 2013
Online resources:
Contents:
Real-Time Digital Signal Processing: Fundamentals, implementations and applications -- Contents -- Preface -- Acknowledgments -- 1 Introduction to Real-Time Digital Signal Processing -- 1.1 Basic Elements of Real-Time DSP Systems -- 1.2 Analog Interface -- 1.2.1 Sampling -- 1.2.2 Quantization and Encoding -- 1.2.3 Smoothing Filters -- 1.2.4 Data Converters -- 1.3 DSP Hardware -- 1.3.1 DSP Hardware Options -- 1.3.2 Digital Signal Processors -- 1.3.3 Fixed- and Floating-Point Processors -- 1.3.4 Real-Time Constraints -- 1.4 DSP System Design -- 1.4.1 Algorithm Development -- 1.4.2 Selection of DSP Hardware -- 1.4.3 Software Development -- 1.4.4 Software Development Tools -- 1.5 Experiments and Program Examples -- 1.5.1 Get Started with CCS and eZdsp -- 1.5.2 C File I/O Functions -- 1.5.3 User Interface for eZdsp -- 1.5.4 Audio Playback Using eZdsp -- 1.5.5 Audio Loopback Using eZdsp -- Exercises -- References -- 2 DSP Fundamentals and Implementation Considerations -- 2.1 Digital Signals and Systems -- 2.1.1 Elementary Digital Signals -- 2.1.2 Block Diagram Representation of Digital Systems -- 2.2 System Concepts -- 2.2.1 LTI Systems -- 2.2.2 The z-transform -- 2.2.3 Transfer Functions -- 2.2.4 Poles and Zeros -- 2.2.5 Frequency Responses -- 2.2.6 Discrete Fourier Transform -- 2.3 Introduction to Random Variables -- 2.3.1 Review of Random Variables -- 2.3.2 Operations of Random Variables -- 2.4 Fixed-Point Representations and Quantization Effects -- 2.4.1 Fixed-Point Formats -- 2.4.2 Quantization Errors -- 2.4.3 Signal Quantization -- 2.4.4 Coefficient Quantization -- 2.4.5 Roundoff Noise -- 2.4.6 Fixed-Point Toolbox -- 2.5 Overflow and Solutions -- 2.5.1 Saturation Arithmetic -- 2.5.2 Overflow Handling -- 2.5.3 Scaling of Signals -- 2.5.4 Guard Bits -- 2.6 Experiments and Program Examples -- 2.6.1 Overflow and Saturation Arithmetic.
2.6.2 Function Approximations -- 2.6.3 Real-Time Signal Generation Using eZdsp -- Exercises -- References -- 3 Design and Implementation of FIR Filters -- 3.1 Introduction to FIR Filters -- 3.1.1 Filter Characteristics -- 3.1.2 Filter Types -- 3.1.3 Filter Specifications -- 3.1.4 Linear Phase FIR Filters -- 3.1.5 Realization of FIR Filters -- 3.2 Design of FIR Filters -- 3.2.1 Fourier Series Method -- 3.2.2 Gibbs Phenomenon -- 3.2.3 Window Functions -- 3.2.4 Design of FIR Filters Using MATLAB® -- 3.2.5 Design of FIR Filters Using the FDATool -- 3.3 Implementation Considerations -- 3.3.1 Quantization Effects in FIR Filters -- 3.3.2 MATLAB® Implementations -- 3.3.3 Floating-Point C Implementations -- 3.3.4 Fixed-Point C Implementations -- 3.4 Applications: Interpolation and Decimation Filters -- 3.4.1 Interpolation -- 3.4.2 Decimation -- 3.4.3 Sampling Rate Conversion -- 3.4.4 MATLAB® Implementations -- 3.5 Experiments and Program Examples -- 3.5.1 FIR Filtering Using Fixed-Point C -- 3.5.2 FIR Filtering Using C55xx Assembly Program -- 3.5.3 Symmetric FIR Filtering Using C55xx Assembly Program -- 3.5.4 Optimization Using Dual-MAC Architecture -- 3.5.5 Real-Time FIR Filtering -- 3.5.6 Decimation Using C and Assembly Programs -- 3.5.7 Interpolation Using Fixed-Point C -- 3.5.8 Sampling Rate Conversion -- 3.5.9 Real-Time Sampling Rate Conversion -- Exercises -- References -- 4 Design and Implementation of IIR Filters -- 4.1 Introduction -- 4.1.1 Analog Systems -- 4.1.2 Mapping Properties -- 4.1.3 Characteristics of Analog Filters -- 4.1.4 Frequency Transforms -- 4.2 Design of IIR Filters -- 4.2.1 Bilinear Transform -- 4.2.2 Filter Design Using the Bilinear Transform -- 4.3 Realization of IIR Filters -- 4.3.1 Direct Forms -- 4.3.2 Cascade Realizations -- 4.3.3 Parallel Realizations -- 4.3.4 Realization of IIR Filters Using MATLAB®.
4.4 Design of IIR Filters Using MATLAB® -- 4.4.1 Filter Design Using MATLAB® -- 4.4.2 Frequency Transforms Using MATLAB® -- 4.4.3 Filter Design and Realization Using the FDATool -- 4.5 Implementation Considerations -- 4.5.1 Stability -- 4.5.2 Finite-Precision Effects and Solutions -- 4.5.3 MATLAB® Implementations of IIR Filters -- 4.6 Practical Applications -- 4.6.1 Recursive Resonators -- 4.6.2 Recursive Quadrature Oscillators -- 4.6.3 Parametric Equalizers -- 4.7 Experiments and Program Examples -- 4.7.1 Direct-Form I IIR Filter Using Floating-Point C -- 4.7.2 Direct-Form I IIR Filter Using Fixed-Point C -- 4.7.3 Cascade IIR Filter Using Fixed-Point C -- 4.7.4 Cascade IIR Filter Using Intrinsics -- 4.7.5 Cascade IIR Filter Using Assembly Program -- 4.7.6 Real-Time IIR Filtering -- 4.7.7 Parametric Equalizer Using Fixed-Point C -- 4.7.8 Real-Time Parametric Equalizer -- Exercises -- References -- 5 Frequency Analysis and the Discrete Fourier Transform -- 5.1 Fourier Series and Fourier Transform -- 5.1.1 Fourier Series -- 5.1.2 Fourier Transform -- 5.2 Discrete Fourier Transform -- 5.2.1 Discrete-Time Fourier Transform -- 5.2.2 Discrete Fourier Transform -- 5.2.3 Important Properties -- 5.3 Fast Fourier Transforms -- 5.3.1 Decimation-in-Time -- 5.3.2 Decimation-in-Frequency -- 5.3.3 Inverse Fast Fourier Transform -- 5.4 Implementation Considerations -- 5.4.1 Computational Issues -- 5.4.2 Finite-Precision Effects -- 5.4.3 MATLAB® Implementations -- 5.4.4 Fixed-Point Implementation Using MATLAB® -- 5.5 Practical Applications -- 5.5.1 Spectral Analysis -- 5.5.2 Spectral Leakage and Resolution -- 5.5.3 Power Spectral Density -- 5.5.4 Convolution -- 5.6 Experiments and Program Examples -- 5.6.1 DFT Using Floating-Point C -- 5.6.2 DFT Using the C55xx Assembly Program -- 5.6.3 FFT Using Floating-Point C -- 5.6.4 FFT Using Fixed-Point C with Intrinsics.
5.6.5 Experiment with the FFT and IFFT -- 5.6.6 FFT Using the C55xx Hardware Accelerator -- 5.6.7 Real-Time FFT Using the C55xx Hardware Accelerator -- 5.6.8 Fast Convolution Using the Overlap-Add Technique -- 5.6.9 Real-Time Fast Convolution -- Exercises -- References -- 6 Adaptive Filtering -- 6.1 Introduction to Random Processes -- 6.2 Adaptive Filters -- 6.2.1 Introduction to Adaptive Filtering -- 6.2.2 Performance Function -- 6.2.3 Method of Steepest Descent -- 6.2.4 LMS Algorithm -- 6.2.5 Modified LMS Algorithms -- 6.3 Performance Analysis -- 6.3.1 Stability Constraint -- 6.3.2 Convergence Speed -- 6.3.3 Excess Mean-Square Error -- 6.3.4 Normalized LMS Algorithm -- 6.4 Implementation Considerations -- 6.4.1 Computational Issues -- 6.4.2 Finite-Precision Effects -- 6.4.3 MATLAB® Implementations -- 6.5 Practical Applications -- 6.5.1 Adaptive System Identification -- 6.5.2 Adaptive Prediction -- 6.5.3 Adaptive Noise Cancellation -- 6.5.4 Adaptive Inverse Modeling -- 6.6 Experiments and Program Examples -- 6.6.1 LMS Algorithm Using Floating-Point C -- 6.6.2 Leaky LMS Algorithm Using Fixed-Point C -- 6.6.3 Normalized LMS Algorithm Using Fixed-Point C and Intrinsics -- 6.6.4 Delayed LMS Algorithm Using Assembly Program -- 6.6.5 Experiment of Adaptive System Identification -- 6.6.6 Experiment of Adaptive Predictor -- 6.6.7 Experiment of Adaptive Channel Equalizer -- 6.6.8 Real-Time Adaptive Prediction Using eZdsp -- Exercises -- References -- 7 Digital Signal Generation and Detection -- 7.1 Sine Wave Generators -- 7.1.1 Lookup Table Method -- 7.1.2 Linear Chirp Signal -- 7.2 Noise Generators -- 7.2.1 Linear Congruential Sequence Generator -- 7.2.2 Pseudo-random Binary Sequence Generator -- 7.2.3 White, Color, and Gaussian Noise -- 7.3 DTMF Generation and Detection -- 7.3.1 DTMF Generator -- 7.3.2 DTMF Detection -- 7.4 Experiments and Program Examples.
7.4.1 Sine Wave Generator Using Table Lookup -- 7.4.2 Siren Generator Using Table Lookup -- 7.4.3 DTMF Generator -- 7.4.4 DTMF Detection Using Fixed-Point C -- 7.4.5 DTMF Detection Using Assembly Program -- Exercises -- References -- 8 Adaptive Echo Cancellation -- 8.1 Introduction to Line Echoes -- 8.2 Adaptive Line Echo Canceler -- 8.2.1 Principles of Adaptive Echo Cancellation -- 8.2.2 Performance Evaluation -- 8.3 Practical Considerations -- 8.3.1 Pre-whitening of Signals -- 8.3.2 Delay Estimation -- 8.4 Double-Talk Effects and Solutions -- 8.5 Nonlinear Processor -- 8.5.1 Center Clipper -- 8.5.2 Comfort Noise -- 8.6 Adaptive Acoustic Echo Cancellation -- 8.6.1 Acoustic Echoes -- 8.6.2 Acoustic Echo Canceler -- 8.6.3 Subband Implementations -- 8.6.4 Delay-Free Structures -- 8.6.5 Integration of Acoustic Echo Cancellation with Noise Reduction -- 8.6.6 Implementation Considerations -- 8.7 Experiments and Program Examples -- 8.7.1 Acoustic Echo Canceler Using Floating-Point C -- 8.7.2 Acoustic Echo Canceler Using Fixed-Point C with Intrinsics -- 8.7.3 Integration of AEC and Noise Reduction -- Exercises -- References -- 9 Speech Signal Processing -- 9.1 Speech Coding Techniques -- 9.1.1 Speech Production Model Using LPC -- 9.1.2 CELP Coding -- 9.1.3 Synthesis Filter -- 9.1.4 Excitation Signals -- 9.1.5 Perceptual Based Minimization Procedure -- 9.1.6 Voice Activity Detection -- 9.1.7 ACELP Codecs -- 9.2 Speech Enhancement -- 9.2.1 Noise Reduction Techniques -- 9.2.2 Short-Time Spectrum Estimation -- 9.2.3 Magnitude Spectrum Subtraction -- 9.3 VoIP Applications -- 9.3.1 Overview of VoIP -- 9.3.2 Discontinuous Transmission -- 9.3.3 Packet Loss Concealment -- 9.3.4 Quality Factors of Media Stream -- 9.4 Experiments and Program Examples -- 9.4.1 LPC Filter Using Fixed-Point C with Intrinsics.
9.4.2 Perceptual Weighting Filter Using Fixed-Point C with Intrinsics.
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Real-Time Digital Signal Processing: Fundamentals, implementations and applications -- Contents -- Preface -- Acknowledgments -- 1 Introduction to Real-Time Digital Signal Processing -- 1.1 Basic Elements of Real-Time DSP Systems -- 1.2 Analog Interface -- 1.2.1 Sampling -- 1.2.2 Quantization and Encoding -- 1.2.3 Smoothing Filters -- 1.2.4 Data Converters -- 1.3 DSP Hardware -- 1.3.1 DSP Hardware Options -- 1.3.2 Digital Signal Processors -- 1.3.3 Fixed- and Floating-Point Processors -- 1.3.4 Real-Time Constraints -- 1.4 DSP System Design -- 1.4.1 Algorithm Development -- 1.4.2 Selection of DSP Hardware -- 1.4.3 Software Development -- 1.4.4 Software Development Tools -- 1.5 Experiments and Program Examples -- 1.5.1 Get Started with CCS and eZdsp -- 1.5.2 C File I/O Functions -- 1.5.3 User Interface for eZdsp -- 1.5.4 Audio Playback Using eZdsp -- 1.5.5 Audio Loopback Using eZdsp -- Exercises -- References -- 2 DSP Fundamentals and Implementation Considerations -- 2.1 Digital Signals and Systems -- 2.1.1 Elementary Digital Signals -- 2.1.2 Block Diagram Representation of Digital Systems -- 2.2 System Concepts -- 2.2.1 LTI Systems -- 2.2.2 The z-transform -- 2.2.3 Transfer Functions -- 2.2.4 Poles and Zeros -- 2.2.5 Frequency Responses -- 2.2.6 Discrete Fourier Transform -- 2.3 Introduction to Random Variables -- 2.3.1 Review of Random Variables -- 2.3.2 Operations of Random Variables -- 2.4 Fixed-Point Representations and Quantization Effects -- 2.4.1 Fixed-Point Formats -- 2.4.2 Quantization Errors -- 2.4.3 Signal Quantization -- 2.4.4 Coefficient Quantization -- 2.4.5 Roundoff Noise -- 2.4.6 Fixed-Point Toolbox -- 2.5 Overflow and Solutions -- 2.5.1 Saturation Arithmetic -- 2.5.2 Overflow Handling -- 2.5.3 Scaling of Signals -- 2.5.4 Guard Bits -- 2.6 Experiments and Program Examples -- 2.6.1 Overflow and Saturation Arithmetic.

2.6.2 Function Approximations -- 2.6.3 Real-Time Signal Generation Using eZdsp -- Exercises -- References -- 3 Design and Implementation of FIR Filters -- 3.1 Introduction to FIR Filters -- 3.1.1 Filter Characteristics -- 3.1.2 Filter Types -- 3.1.3 Filter Specifications -- 3.1.4 Linear Phase FIR Filters -- 3.1.5 Realization of FIR Filters -- 3.2 Design of FIR Filters -- 3.2.1 Fourier Series Method -- 3.2.2 Gibbs Phenomenon -- 3.2.3 Window Functions -- 3.2.4 Design of FIR Filters Using MATLAB® -- 3.2.5 Design of FIR Filters Using the FDATool -- 3.3 Implementation Considerations -- 3.3.1 Quantization Effects in FIR Filters -- 3.3.2 MATLAB® Implementations -- 3.3.3 Floating-Point C Implementations -- 3.3.4 Fixed-Point C Implementations -- 3.4 Applications: Interpolation and Decimation Filters -- 3.4.1 Interpolation -- 3.4.2 Decimation -- 3.4.3 Sampling Rate Conversion -- 3.4.4 MATLAB® Implementations -- 3.5 Experiments and Program Examples -- 3.5.1 FIR Filtering Using Fixed-Point C -- 3.5.2 FIR Filtering Using C55xx Assembly Program -- 3.5.3 Symmetric FIR Filtering Using C55xx Assembly Program -- 3.5.4 Optimization Using Dual-MAC Architecture -- 3.5.5 Real-Time FIR Filtering -- 3.5.6 Decimation Using C and Assembly Programs -- 3.5.7 Interpolation Using Fixed-Point C -- 3.5.8 Sampling Rate Conversion -- 3.5.9 Real-Time Sampling Rate Conversion -- Exercises -- References -- 4 Design and Implementation of IIR Filters -- 4.1 Introduction -- 4.1.1 Analog Systems -- 4.1.2 Mapping Properties -- 4.1.3 Characteristics of Analog Filters -- 4.1.4 Frequency Transforms -- 4.2 Design of IIR Filters -- 4.2.1 Bilinear Transform -- 4.2.2 Filter Design Using the Bilinear Transform -- 4.3 Realization of IIR Filters -- 4.3.1 Direct Forms -- 4.3.2 Cascade Realizations -- 4.3.3 Parallel Realizations -- 4.3.4 Realization of IIR Filters Using MATLAB®.

4.4 Design of IIR Filters Using MATLAB® -- 4.4.1 Filter Design Using MATLAB® -- 4.4.2 Frequency Transforms Using MATLAB® -- 4.4.3 Filter Design and Realization Using the FDATool -- 4.5 Implementation Considerations -- 4.5.1 Stability -- 4.5.2 Finite-Precision Effects and Solutions -- 4.5.3 MATLAB® Implementations of IIR Filters -- 4.6 Practical Applications -- 4.6.1 Recursive Resonators -- 4.6.2 Recursive Quadrature Oscillators -- 4.6.3 Parametric Equalizers -- 4.7 Experiments and Program Examples -- 4.7.1 Direct-Form I IIR Filter Using Floating-Point C -- 4.7.2 Direct-Form I IIR Filter Using Fixed-Point C -- 4.7.3 Cascade IIR Filter Using Fixed-Point C -- 4.7.4 Cascade IIR Filter Using Intrinsics -- 4.7.5 Cascade IIR Filter Using Assembly Program -- 4.7.6 Real-Time IIR Filtering -- 4.7.7 Parametric Equalizer Using Fixed-Point C -- 4.7.8 Real-Time Parametric Equalizer -- Exercises -- References -- 5 Frequency Analysis and the Discrete Fourier Transform -- 5.1 Fourier Series and Fourier Transform -- 5.1.1 Fourier Series -- 5.1.2 Fourier Transform -- 5.2 Discrete Fourier Transform -- 5.2.1 Discrete-Time Fourier Transform -- 5.2.2 Discrete Fourier Transform -- 5.2.3 Important Properties -- 5.3 Fast Fourier Transforms -- 5.3.1 Decimation-in-Time -- 5.3.2 Decimation-in-Frequency -- 5.3.3 Inverse Fast Fourier Transform -- 5.4 Implementation Considerations -- 5.4.1 Computational Issues -- 5.4.2 Finite-Precision Effects -- 5.4.3 MATLAB® Implementations -- 5.4.4 Fixed-Point Implementation Using MATLAB® -- 5.5 Practical Applications -- 5.5.1 Spectral Analysis -- 5.5.2 Spectral Leakage and Resolution -- 5.5.3 Power Spectral Density -- 5.5.4 Convolution -- 5.6 Experiments and Program Examples -- 5.6.1 DFT Using Floating-Point C -- 5.6.2 DFT Using the C55xx Assembly Program -- 5.6.3 FFT Using Floating-Point C -- 5.6.4 FFT Using Fixed-Point C with Intrinsics.

5.6.5 Experiment with the FFT and IFFT -- 5.6.6 FFT Using the C55xx Hardware Accelerator -- 5.6.7 Real-Time FFT Using the C55xx Hardware Accelerator -- 5.6.8 Fast Convolution Using the Overlap-Add Technique -- 5.6.9 Real-Time Fast Convolution -- Exercises -- References -- 6 Adaptive Filtering -- 6.1 Introduction to Random Processes -- 6.2 Adaptive Filters -- 6.2.1 Introduction to Adaptive Filtering -- 6.2.2 Performance Function -- 6.2.3 Method of Steepest Descent -- 6.2.4 LMS Algorithm -- 6.2.5 Modified LMS Algorithms -- 6.3 Performance Analysis -- 6.3.1 Stability Constraint -- 6.3.2 Convergence Speed -- 6.3.3 Excess Mean-Square Error -- 6.3.4 Normalized LMS Algorithm -- 6.4 Implementation Considerations -- 6.4.1 Computational Issues -- 6.4.2 Finite-Precision Effects -- 6.4.3 MATLAB® Implementations -- 6.5 Practical Applications -- 6.5.1 Adaptive System Identification -- 6.5.2 Adaptive Prediction -- 6.5.3 Adaptive Noise Cancellation -- 6.5.4 Adaptive Inverse Modeling -- 6.6 Experiments and Program Examples -- 6.6.1 LMS Algorithm Using Floating-Point C -- 6.6.2 Leaky LMS Algorithm Using Fixed-Point C -- 6.6.3 Normalized LMS Algorithm Using Fixed-Point C and Intrinsics -- 6.6.4 Delayed LMS Algorithm Using Assembly Program -- 6.6.5 Experiment of Adaptive System Identification -- 6.6.6 Experiment of Adaptive Predictor -- 6.6.7 Experiment of Adaptive Channel Equalizer -- 6.6.8 Real-Time Adaptive Prediction Using eZdsp -- Exercises -- References -- 7 Digital Signal Generation and Detection -- 7.1 Sine Wave Generators -- 7.1.1 Lookup Table Method -- 7.1.2 Linear Chirp Signal -- 7.2 Noise Generators -- 7.2.1 Linear Congruential Sequence Generator -- 7.2.2 Pseudo-random Binary Sequence Generator -- 7.2.3 White, Color, and Gaussian Noise -- 7.3 DTMF Generation and Detection -- 7.3.1 DTMF Generator -- 7.3.2 DTMF Detection -- 7.4 Experiments and Program Examples.

7.4.1 Sine Wave Generator Using Table Lookup -- 7.4.2 Siren Generator Using Table Lookup -- 7.4.3 DTMF Generator -- 7.4.4 DTMF Detection Using Fixed-Point C -- 7.4.5 DTMF Detection Using Assembly Program -- Exercises -- References -- 8 Adaptive Echo Cancellation -- 8.1 Introduction to Line Echoes -- 8.2 Adaptive Line Echo Canceler -- 8.2.1 Principles of Adaptive Echo Cancellation -- 8.2.2 Performance Evaluation -- 8.3 Practical Considerations -- 8.3.1 Pre-whitening of Signals -- 8.3.2 Delay Estimation -- 8.4 Double-Talk Effects and Solutions -- 8.5 Nonlinear Processor -- 8.5.1 Center Clipper -- 8.5.2 Comfort Noise -- 8.6 Adaptive Acoustic Echo Cancellation -- 8.6.1 Acoustic Echoes -- 8.6.2 Acoustic Echo Canceler -- 8.6.3 Subband Implementations -- 8.6.4 Delay-Free Structures -- 8.6.5 Integration of Acoustic Echo Cancellation with Noise Reduction -- 8.6.6 Implementation Considerations -- 8.7 Experiments and Program Examples -- 8.7.1 Acoustic Echo Canceler Using Floating-Point C -- 8.7.2 Acoustic Echo Canceler Using Fixed-Point C with Intrinsics -- 8.7.3 Integration of AEC and Noise Reduction -- Exercises -- References -- 9 Speech Signal Processing -- 9.1 Speech Coding Techniques -- 9.1.1 Speech Production Model Using LPC -- 9.1.2 CELP Coding -- 9.1.3 Synthesis Filter -- 9.1.4 Excitation Signals -- 9.1.5 Perceptual Based Minimization Procedure -- 9.1.6 Voice Activity Detection -- 9.1.7 ACELP Codecs -- 9.2 Speech Enhancement -- 9.2.1 Noise Reduction Techniques -- 9.2.2 Short-Time Spectrum Estimation -- 9.2.3 Magnitude Spectrum Subtraction -- 9.3 VoIP Applications -- 9.3.1 Overview of VoIP -- 9.3.2 Discontinuous Transmission -- 9.3.3 Packet Loss Concealment -- 9.3.4 Quality Factors of Media Stream -- 9.4 Experiments and Program Examples -- 9.4.1 LPC Filter Using Fixed-Point C with Intrinsics.

9.4.2 Perceptual Weighting Filter Using Fixed-Point C with Intrinsics.

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