采样和量化之间的差异

Sampling vs Quantization

In digital signal processing and related fields, sampling and quantization are two methods, rather steps, used in the discretization of an analog signal in converting it to a digital signal. With the advent of electronics and computers, almost all the technological functions are digitized so they can be handled by computers or other digital systems. These two are key ideas in analog to digital conversion.

What is Sampling?

In digital signal processing, sampling is the process of breaking up a continuous signal to a discrete signal. A common usage of the process is the analog to digital conversion of a sound signal. The process breaks up the sound wave into intervals along the time axis to produce a sequence of signals. As a result, the values in the time axis are converted from continuous, to discrete values with corresponding magnitudes. The sampled signal is known as the Pulse Amplitude Modulated Signal.

During the process, within a defined time interval T, a single maximum amplitude (a sample) is selected to represent the whole interval. So rather having a continuous signal, the process develops a signal with single amplitude representing the whole time interval. However, still the magnitude of the amplitude is continuous. The component of the system that executes this process is known as the sampler.

即使该信号现在在X轴中具有离散值，信号是连续的一半，并且不能以数字方式正确表示。为了达到完全离散的信号，进行了离散化的第二步。

What is Quantization?

In digital signal processing, quantization is the process of mapping a larger set of values to a smaller set. The best example is rounding the numbers to make them manageable. Consider the weight of a batch of chocolate balls. They weigh somewhere between 4.99 grams and 5.20 grams. Rather than stating them individually it is a good representation if we say the chocolate balls weigh 5.00 grams. To do this, the weight of the balls has to be either rounded up or down. The same argument applies when saying the shoes were $15.00, even though the price tag was $ 14.99.

Applying this to signals, the partially discretized signal already has a single continuous value representing each interval of time in the pulse amplitude modulated signal. In the quantization process, the amplitude values are either rounded up or down to the nearest predetermined value. The result is that, rather than the amplitude of signals having infinitely many values, they are narrowed to a much smaller set of values. This type of signal is known as Pulse Code Modulated Signal.

What is the difference between Sampling and Quantization?

• In sampling, the time axis is discretized while, in quantization, y axis or the amplitude is discretized.

• In the sampling process, a single amplitude value is selected from the time interval to represent it while, in quantization, the values representing the time intervals are rounded off, to create a finite set of possible amplitude values.

• Sampling is done prior to the quantization process.