Audio Signal

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Audio Signal

• Computer Application in Music

Lecture III
Sep. 11, 2008
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Audio Signal

• Audio signal is a representation of sound wave.
• The amplitude of the sound wave is represented by
  voltage or magnetic intensity in stead of sound
  intensity

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Audio Signal

• This is what actually happened in air and what we
  hear.

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Audio Signal

• The sound wave is translated and represented by
  an electrical signal.

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Analog Signal

• Time continuous signal x(t)

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Analog Signal
The signal coming out of a microphone is an
analog signal.
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Digital signal

• Time discrete signal
• Digital signal can be derived by sampling and
  quantizing the analog signal.

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Digital signal - sampling

• Sampling converts a continuous-time signal to a
  discrete-time signal.

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Digital signal - sampling

• The duration between each two adjacent samples Ts
  is constant

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Digital signal - sampling

• This can be described as for each Ts time we
  take one sample out of the original signal.
• The sequence of samples is called digital signal.
• If the original signal is x(t), then the signal
  after sampling can be expressed as

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Digital signal sampling rate

• Sampling rate is defined as the number of samples
  obtained in one second.
• The larger the sampling frequency is, the more
  samples we have in one second, the more accurate
  the sampled signal is, compared to the original
  signal.

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Nyquist Frequency

• Nyquist frequency is defined as half of the
  sampling rate.
• For any analog signal that we want to sample, to
  avoid aliasing distortion, the Nyquist frequency
  cannot be lower than the maximal frequency of
  this signal.

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Nyquist Frequency
FN Nyquist frequency Fs sampling rate Fs 2FN
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Aliasing

• Aliasing refers to the distortion effect that
  results when Nyquist frequency is smaller than
  the maximum frequency of the original signal (or
  the sampling frequency is lower than twice the
  maximum frequency of the signal).

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Aliasing

• To avoid aliasing, the Nyquist has to be greater
  than the highest frequency component of the
  signal.
• Nyquist Frequency gt maximum frequency

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Quantization and Bit resolution

• Quantization refers to the process to approximate
  the sampled signals amplitude values to a set of
  integer values.
• The number of the integer values is determined
  by the required bit resolution.
• Bit resolution refers to the number of bits used
  to describe each sample in a digital binary
  format.

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The quantization process

• 3 bit quantization

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Quantization

• Why do we need the quantization process?

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Quantization

• Why do we need the quantization process?
• We dont want a very large set of data.

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Bit

• What is bit?

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Bit

• What is bit?
• Bit is binary digit, represented by 1 or 0.

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Bit

• Why binary?

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Bit

• Why binary?
• Binary is the only thing that computers and
  digital systems can recognize. The machine cannot
  recognize a digit streaming like
• 12.4352, 23.1011, 9.2345, 3.5112, 9.1032,
  0.3422,
• We need to convert all the data into binary
  digits, with N bits representing each value. N is
  determined by the systems bit resolution.

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Quantization error

• Since quantization is an approximating process,
  it will generate errors. The signal-to-noise
  ratio of a quantized signal with M bit resolution
  can be expressed as
• Therefore, when increasing one bit, we can get
  approximately 6 dB signal-to-noise ratio.
• Notice that the noise here is the quantization
  noise caused by the approximation during the
  quantization process. It differs from other types
  of noise such as noise caused by the electrical
  equipments.

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Analog-to-digital converter

• Analog-to-digital converter (ADC) is a system to
  convert analog signal to digital signal.
• ADC includes the whole process of sampling and
  quantization.

Analog signal
digital signal
ADC
101100011110100101100
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Digital-to-analog converter

• DAC is the reverse version of ADC. It converts
  digital signal to analog signal

digital signal
analog signal
DAC
0101100011110100101100
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Analog recording

• Analog recording is the technique to record sound
  wave as continuous signal in the media, such as
  magnetic tapes or phonograph record.

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Digital recording

• Digital recoding is the technique to record sound
  waves into digital signal format.

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Analog vs. digital

• Since digital audio technology emerged, theres
  always been an argument about analog audio versus
  digital audio.

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Analog vs. digital

• Since digital audio technology emerged, theres
  always been an argument about analog audio versus
  digital audio.
• Disadvantage of digital
• Aliasing distortion
• Quantization noise

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Analog vs. digital

• Since digital audio technology emerged, theres
  always been an argument about analog audio versus
  digital audio.
• Disadvantage of digital
• Aliasing distortion
• Quantization noise
• Disadvantage of analog
• Noise added by the analog system
• Wow and flutter

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Analog vs. digital

• In terms of accuracy
• Accurate reproduction can be made in any digital
  system.
• For analog audio signal, the accuracy of the
  signal reproduction highly depends on the
  performance of the analog equipments.

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Analog vs. digital

• In terms of sound quality
• The accuracy of analog audio signal highly
  depends on the analog systems that reproduce the
  sound. However, sound quality is more like a
  subjective term. Some audio engineers like the
  colors that the analog equipments have, however
  those colors cause the inaccurate reproduction
  of the signal.

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Analog vs. digital

• Digital takes over?
• Digital signal comes from sampling the analog
  signal. There can never be only digital signal.
  In terms of producing sounds, digital systems can
  do everything that analog system intends to do
  while keeping a high accuracy.

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Data compression

• Data compression refers to the process to use
  fewer data to represent the same information.
• There are many data compression methods for audio
  and video signal such as MP3 and JPEG. For
  example, in the quantization process, if we
  downgrade the bit resolution from 16bit to 14bit,
  we will get less data, however lose the SNR by
  12dB.

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Masking

• Masking refers to the effect that the perception
  of one sound is affected by another sound.
• How effective one sound can mask another depends
  on both of the frequencies of these two sounds.

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MP3

• MP3 is a data-compressed audio format.
• The data compression method of MP3 utilizes the
  masking effect. It compresses the sounds that are
  masked by others and cannot be perceived.
• MP3 technology largely decreased the data volume
  of audio files with this compression method.