Recording - Quantizarion

Question 1

What determents the number of quantization steps?

Answer 1

• defined by the number of bits used to represent the value of the function
• number of quantizations levels: 2B for B bits

Question 2

What is the Quantization Error?

Answer 2

Approximation error nj between real value fj′ and discretized value fj

Question 3

What is the signal-to-noise ratio?

Answer 3

• standardized way to express the noise in a system/sensor
• In the context of pattern recognition:
ratio of the expected signal over the expected quantization noise
• uncertainty about the input signal
You want a high signal-to-noise ratio.

Question 4

What is or could be the influence of the number of Bits on the quantization error?

Answer 4

Under certain assumptions: SNR is directly proportional to
the number of bits B
SNRdB =r =6·B−7.2
1. zero-mean signal and noise
2. number of quantization bins large enough, such that the error n is uniformly distributed p(n) = 􏰘 1/s for − 2/s ≤ n ≤ 2/s otherwise 0
3. limited range of the signal values: −4σf′ ≤f′≤4σf′

Question 5

What is the SNR criterion?

Answer 5

determines how many bits to use, but not how to use them

Question 6

What is the optimal quantization characteristic?

Answer 6

choose aν and bν such that ε is minimized

Question 7

What is Pulse Code Modulation (PCM)?

Answer 7

A linear quantization characteristic (with equally spaced quantization levels) is optimal if and only if the signal amplitudes are equally distributed.
Coding based on the methods described so far (sampling & quantization) is called Pulse Code Modulation