Audio Signal Processing

1
Audio Signal Processing

• Shyh-Kang Jeng
• Department of Electrical Engineering/
• Graduate Institute of Communication Engineering
• Reference Marina Bosi, Perceptual Audio
  Coding-Lecture Note of Music 422/EE367C,
• CCRMA, Stanford University, Spring 1999

2
Contents

• Introduction
• Quantization
• Time to Frequency Mapping
• Psychoacoustics
• Bit Allocation
• Perceptual Audio Coders
• MPEG-1 Audio

3
Audio Signal Processing-- Introduction

• Shyh-Kang Jeng
• Department of Electrical Engineering/
• Graduate Institute of Communication Engineering

4
Outline

• Overview of audio coder
• Representation of audio signals

5
Audio Coder
Encode
10010101
Decode
10010101
6
Audio Coding

• Audio coder (Codec)
• Input audio signal
• Output audio signal perceptually close to the
  input signal
• Beginning of the coding chain
• Source modeling to optimize signal representation
• Last stage
• Modeling of ear and processing of signals to
  minimize the irrelevant data

7
Coding Goals

• Maximize the perceived quality of the sound
• Minimize the data rates and complexity
• Related parameters
• Delay
• Error robustness
• Scalability
• etc.

8
Pulse-Code Modulation

• PCM Encoder
• PCM Decoder

Qnantize
Sample
0101010
-1
Quantize
Interpolate
0101010
9
PCM Example CD Format

• Sampling frequency Fs 44.1 KHz (i.e. one
  sample every 0.023 ms)
• Number of bits per sample R 16 (i.e. up to
  65536 levels)
• Bit rate I FsR 706.5 kb/s per channel
• Total bit rate 1.413 Mb/s
• Signal to noise ratio SNR 90 dB

10
Potential Coding Errors

• Sampling error (aliasing)
• Quantization error
• Overload error
• Round-off error
• Transmission/storage error

11
Transform Coder
PCM Encoder
Transform Bit Allocation
010
0101010
Bit Allocation Transform
PCM Decoder
0101010
010
12
Why Transform Coders?

• Reduce redundancies
• Transformation to frequency domain can reduce
  redundancies for tonal signals (e.g., music,
  speech)
• Reduce irrelevancies
• For example, sounds too low to hear or sounds
  masked by louder sounds need not be coded as
  accurate as the other parts
• Reduce bit-rate

13
Fourier Transform

• Fourier transform
• Inverse Fourier transform

14
Energy and Power

• Power
• Energy

15
Parsevals Theorem

• For signals that have finite energy in the time
  domain,
• power spectral density
• The power spectral density gives a way to compare
  the strength of different components of a signal

16
Signal Sampling
17
Aliasing
18
Sampling Theorem
0
f
s
19
Eliminating Aliasing

• If your application requires a sample rate below
  the highest frequencies in the signal, you will
  need to low pass filter the signal before
  sampling
• Example The telephone sample rate is 8 KHz and a
  4 KHz low pass filter is employed. (speech 100
  Hz to 7 KHz, you really do sound different on
  the phone)

20
Coder Implications

• We can only hear up to 20 KHz so we should
  filter out higher frequencies and sample at 40
  KHz to get high quality reproductions of
  broadband sound
• For example, CDs sample at 44.1 KHz and provide
  much greater sound quality than telephone system