Digital Audio Theory

1 Introduction

1.1 Describing audio signals

1.2 Digital audio basics

1.3 Describing audio systems

1.4 Further reading

1.5 Challenges

1.6 Project - audio playback

2 Complex vectors and phasors

2.1 Complex number representation and operations

2.2 Complex conjugates

2.3 Phasors

2.4 Beat frequencies

2.5 Challenges

2.6 Project - AM and FM synthesis

Bibliography

3 Sampling

3.1 Phasor representation on the complex plane

3.2 Nyquist frequency

3.3 Time shift operators

3.4 Sampling a continuous signal

3.5 Jitter

3.6 Challenges

Bibliography

4 Aliasing and reconstruction

4.1 Under-sampling

4.2 Predicting the alias frequency

4.3 Anti-aliasing filter

4.4 Reconstruction

4.5 Challenges

4.6 Project - aliasing

Bibliography

5 Quantization

5.1 Quantization resolution

5.2 Audio buffers

5.3 Sample-and-hold circuit

5.4 Quantization error (eq)

5.5 Pulse code modulation

5.6 Challenges

Bibliography

6 Dither

6.1 Signal-to-Error Ratio (SER)

6.2 SER at low signal levels

6.3 Applying dither

6.4 Triangular PDF dither

6.5 High-frequency dither

6.6 Challenges

6.7 Project - dither effects

Bibliography

7 DSP basics

7.1 Time-shift operators

7.2 Time-reversal operator

7.3 Time scaling

7.4 Block diagrams

7.5 Difference equations

7.6 Canonical form

7.7 Challenges

7.8 Project - plucked string model

Bibliography

8 FIR filters

8.1 FIR filters by way of example

8.2 Impulse response

8.3 Convolution

8.4 Cross-correlation

8.5 FIR filter phase

8.6 Designing FIR filters

8.7 Challenges

8.8 Project - FIR filters

Bibliography

9 z-Domain

9.1 Frequency response

9.2 Magnitude response

9.3 Comb filters

9.4 z-Transform

9.5 Pole/zero plots

9.6 Filter phase response

9.7 Group delay

9.8 Challenges

10 IIR filters

10.1 General characteristics of IIR filters

10.2 IIR filter transfer functions

10.3 IIR filter stability

10.4 Second-order resonators

10.5 Biquadratic filters

10.6 Proportional parametric EQ

10.7 Forward-reverse filtering

10.8 Challenges

10.9 Project - resonator

Bibliography

11 Impulse response measurements

11.1 Noise reduction through averaging

11.2 Capturing IRs with MLS

11.3 Capturing IRs with ESS

11.4 Challenges

11.5 Project - room response measurements

Bibliography

12 Discrete Fourier transform

12.1 Discretizing a transfer function

12.2 Sampling the frequency response

12.3 The DFT and inverse discrete Fourier transform

12.4 Twiddle factor

12.5 Properties of the DFT

12.6 Revisiting sampling in the frequency domain

12.7 Frequency interpolation

12.8 Challenges

12.9 Project - spectral filtering

13 Real-time spectral processing

13.1 Filtering in the frequency domain

13.2 Windowing

13.3 Constant overlap and add

13.4 Spectrograms

13.5 Challenges

13.6 Project - automatic feedback control

14 Analog modeling

14.1 Derivation of the z-transform

14.2 Impulse invariance

14.3 Bilinear transformation

14.4 Frequency sampling

14.5 Non-linear modeling with ESS

14.6 Challenges

Bibliography