Quantization is the process of mapping input values from a large set to output values in a smaller set, often with a finite number of elements. Quantization is the opposite of sampling. It is done on the y-axis.
When you are quantizing an image, you are actually dividing a signal into quanta partitions. On the x axis of the signal, are the coordinate values and on the y-axis, we have amplitudes. Therefore, digitizing the amplitudes is what is referred to as quantization.
As a result, the values on x-axis time intervals are converted from continuous, to discrete values, with each Time interval corresponding to a specific value of amplitude. So, instead of having a continuous analog signal, a new digitalized signal is produced with single maximum amplitude, representing the whole time interval.
The resulting signal is called the Pulse Amplitude Modulated Signal, which is half continuous and cannot be represented digitally. So, a second step of discretization, called quantization, is carried out. Image courtesy: music. 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.
Even though the signal has discrete values in x axis now, the signal is half continuous and cannot be correctly represented digitally. In order to achieve a completely discrete signal, a second step of discretization is carried out. Figure 5. The samples from Fig. Nyquist Sampling Rate A signal should be sampled at a rate greater than twice its maximum frequency.
Figure 6. In contrast, if a sinusoidal signal is sampled with a low sampling rate, the samples may be too infrequent to recover the original signal. Figure 7. Figure 8. Since there is a sample at every peak and trough of the sinusoid, there is no lower frequency sinusoid that fits these samples.
Figure 9. Since all the samples are at the zero crossings, ideal low pass filtering produces a zero signal instead of recovering the sinusoid. The Nyquist-Shannon sampling theorem states that the sampling rate for exact recovery of a signal composed of a sum of sinusoids is larger than twice the maximum frequency of the signal. To learn more about sampling and the Nyquist-Shannon theorem, read Sampling: what Nyquist didn't say, and what to do about it by Tim Wescott.
Quantization Quantizing samples to levels and then to sequences of bits leads to quantization error.
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