The document discusses quantization, which is the process of mapping continuous values to a smaller set of discrete values. It specifically discusses quantizing signals in digital signal processing and simulation. There are two main types of quantization: uniform and non-uniform. Uniform quantization spaces the quantization levels uniformly, while non-uniform uses a logarithmic relation. Quantization introduces errors from approximating values, called quantization error. Quantization noise refers specifically to the error created when continuously changing analog audio signals are quantized to digital. MATLAB code is provided as an example to quantize and plot a sampled sine wave to illustrate quantization error.

1. Quantitation MATLAB code
- Quantization is the process of mapping continuous infinite values to a smaller set of
discrete finite values. In the context of simulation and embedded computing, it is
about approximating real-world values with a digital representation that introduces
limits on the precision and range of a value.
- Quantization is involved to degree in all digital signal processing, as the process of
representing a signal in digital form ordinarily involves rounding.
- The simplest way to quantize a signal is to choose the digital amplitude value closest
to the original analogue amplitude. This example shows the original analogue signal
(green), the quantized signal (black dots), the signal reconstructed from the
quantized signal (yellow) and the difference between the original signal and the
reconstructed signal (red). The difference between the original signal and the
reconstructed signal is the quantization error and, in this simple quantization
scheme, is a deterministic function of the input signal.
There are two types of Quantization
- Uniform Quantization
- Non-uniform Quantization.
- The type of quantization in which the quantization levels are uniformly spaced
termed as a Uniform Quantization and unequal and mostly the relation between
them is logarithmic, termed as a Non-uniform Quantization.
- There are two types of uniform quantization. They are Mid-Rise type and Mid-
Tread type. The following figures represent the two types of uniform quantization.

2. - The Mid-Rise type called because the origin lies in the middle of a raising part
of the staircase like graph. The quantization levels in this type are even in
number.
- The Mid-tread type called because the origin lies in the middle of a tread of
the staircase like graph. The quantization levels in this type are odd in
number.
- Both the mid-rise and mid-tread type of uniform quantizers are symmetric
about the origin.
Quantization Error
- For any system, during its functioning, there is always a difference in the
values of its input and output. The processing of the system results in an
error, which is the difference of those values.
- The difference between an input value and its quantized value called
a Quantization Error. A Quantizer is a logarithmic function that performs
Quantization rounding off the value rounding off the value. An analogue-to-
digital converter (ADC) works as a quantizer.
- The following figure illustrates an example for a quantization error,
indicating the difference between the original signal and the quantized signal.
Quantization Noise
It is a type of quantization error, which usually occurs in analogue audio signal, while
quantizing it too digital. For example, in music, the signals keep changing
continuously, where a regularity not found in errors. Such errors create a wideband
noise called as Quantization Noise.

3. MATLAB code

4. - This example illustrates the nature of scalar quantization more clearly.
After quantizing a sampled sine wave, it plots the original and
quantized signals. The plot contrasts the x's that make up the sine
curve with the dots that make up the quantized signal. The vertical
coordinate of each dot is a value in the vector codebook.