CS485 Sylabus

### Application of the Nyquist Rate: digital CD quality audio

• Nyquist rate to obtain digital CD quality audio

• Problem description:

 We want to store music (which is analog data) as a computer file (which is digital data)

• Question:

 How fast do you need to sample to reconstruct audible audio waves completely accurately ?

• Pre-requisite: a fact from Biology

 Human ear can hear sound waves with frequency ≤ 20,000 Hz

• The Nyquist sampling rate for human audible signal:

 ``` Nyquist Sampling Rate = 2 × MaxFrequency (MaxFreq = 20,000 Hz) = 2 × 20000 Hz = 40000 Hz (Meaning: 40000 samples per second) ```

Note:

 ``` 1 Hz (Hertz) = 1 event (sample) per second ```

• Sampling rate used by the music industry

• Digital music:

 Digital music = audio (music) stored in digital format Use sampling to convert audio to digital !!!

• Sampling rate used by the music industry:

• The sample rate used to obtain CD quality audio is: 44100 Hz

(This rate is higher than the Nyquist rate of 40,000 Hz)

• The reason is historical:

 The sampling rate of 44.1 kHz was inherited from recording method they already used in video cassettes Reference: click here

• Encoding CD quality audio

• Encoding standard quality audio:

• Normally, an audio sample (= the amplitude value of the audio signal) is encoded using 8 bits (as a signed binary number)

Example:

• Encoding CD quality audio:

• In CD quality audio, an audio sample is encoded using 16 bits (signed binary number)

Example:

(Result: highly accurate representation of the original audio signal, but will require more storage)

• Data rate of CD-quality audio

• Data rate of mono CD quality audio:

 ``` Sample Rate = 44,100 Hz (i.e., we sample 44,100 times in 1 sec) ====> 44,100 samples in 1 sec 1 sample is encoded using 16 bits ====> 44,100 × 16 = 705,600 bits in 1 sec Data rate of (mono) CD quality audio = 705,600 bits/sec ```

• Data rate of mono CD quality audio:

 ``` 2 channels used for stereo ====> 2 × 705,600 bits = 1,411,200 bits/sec ```