- 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
- Digital music:
- Digital music =
audio (music) stored
in digital format
- Use sampling to convert audio to digital !!!
- Digital music =
audio (music) stored
in digital format
- 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
- The sampling rate
of 44.1 kHz was
inherited from
recording method they
already used in
video cassettes
- The sample rate
used to obtain CD quality audio
is:
44100 Hz
- 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:
- Normally, an audio sample
(= the amplitude value of the
audio signal)
is encoded using
8 bits
(as a signed binary number)
- 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)
- In CD quality audio,
an audio sample is
encoded using
16 bits
(signed binary number)
- 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