Implications of Sample Rate and Bit Size

Affects Quality of Audio

• Ears do not respond to sound in a linear fashion
• Decibel (dB) a logarithmic measurement of sound
• 16-Bit has a signal-to-noise ratio of 98 dB -- virtually inaudible
• 8-bit has a signal-to-noise ratio of 50 dB
• Therefore, 8-bit is roughly 8 times as noisy
  • 6 dB increment is twice as loud

Signal to Noise Ratio (SNR)

• In any analog system, some of the voltage is what you want to measure ( signal), and some of it is random fluctuations (noise).

• Ratio of the power of the two is called the signal to noise ratio (SNR). SNR is a measure of the quality of the signal.

• SNR is usually measured in decibels (dB).

  $SNR = 10 \log \frac{V_{signal}^2}{V_{noise}^2} = 20 \log \frac{V_{signal}}{V_{noise}}$

• Typically 8 bits or 16 bits.

• Each bit adds about 6 dB of resolution, so 16 bits => 96 dB.

• Samples are typically stored as raw numbers (linear format ), or as logarithms (u-law (or A-law in Europe)).
  • Logarithmic representation approximates perceptual uniformity.

Affects Size of Data

There is therfore is a trade off between Audio Quality vs. Data Rate

Some typical applications of sample bit size and sample rate are listed below:

Quality    Sample Rate  Bits per   Mono/        Data Rate        Frequency
	      (KHz)      Sample    Stereo     (Uncompressed)       Band
---------  -----------	--------  --------   -----------------  ------------

Telephone     8            8        Mono       8   KBytes/sec   200-3,400 Hz

AM Radio     11.025        8        Mono      11.0 KBytes/sec

FM Radio     22.050       16       Stereo     88.2 KBytes/sec

CD           44.1         16       Stereo    176.4 KBytes/sec   20-20,000 Hz

DAT          48           16       Stereo    192.0 KBytes/sec   20-20,000 Hz

AUDIO DEMO: Comparison of Sample Rate and Bit Size

Click on the file links below to audibly hear the difference in the sampling rates/bit sizes indicated for each file type:

File Type	File Size (all mono)
44Hz 16 bit	3.5 Mb
44KHz 8-bit	1.3 Mb
22 KHz 16-bit	740 Kb
22KHz 8-Bit	424 Kb
11KHz 8-bit	120 K

• Telephone uses u-law encoding, others use linear. So the dynamic range of digital telephone signals is effectively 13 bits rather than 8 bits.
• CD quality stereo sound -> 10.6 MB / min.

Practical Implications of Nyquist Sampling Theory

• Must (low pass) filter signal before sampling:

  

  Practical Implication of Nyquist;Must Low Pass Filter Signal before Sampling

• Otherwise strange artifacts from high frequency signals appear and are audible.

We'll finish off with a question: Why are CD Sample Rates 44.1 KHz?

The answer should be obvious if you have paid attention to the above notes (Answer in Lecture).