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# Quantization Errors

### Key Takeaways

• The two processes involved in analog-to-digital conversion are sampling and quantization.

• The quality of the quantized waveform depends on the number of levels.

• If the step size is greater between two consecutive levels, the difference between the analog signal and the quantized discrete values becomes high and results in more quantization errors. If the step size is greater between two consecutive levels, the difference between the analog signal and the quantized discrete values becomes high and results in more quantization errors

Sampling and quantization are two processes that make up the soul of digital signal processing. Quantization maps the continuous analog values to discrete digital values. In a sampling instant, the difference between the analog signal and the closest available digital signal corresponds to a quantization error. The quantization process sources noise into the sample signal, and the noise is generally termed quantization noise.

## Sampling and Quantization

We often talk about the advantages of digital systems, digital communication, etc. by comparing them with analog systems. In digital systems, the continuous analog signals are converted into discrete finite-value signals. Sampling and quantization are the two processes involved in this analog-to-digital conversion. ## Quantization Process

The quantization process represents the signal sampled by a fixed number of bits. The quantization process involves the comparison of the analog signal values to a set of predefined values. A unique binary number is associated with each level. This binary number is the closest digital value available to the level under consideration. Quantization results in the approximation of the analog signal to the digital signal.

Quantization is an inevitable process in analog to digital conversion. The three advantages of quantization are: ## How Can Quantization Be Performed?

The figure below shows the signal getting quantized. The quality of the quantized waveform is dependent on the number of levels. The digital amplitude of the quantized output is called reconstruction levels or representation levels. Two adjacent levels are separated by a space called quantum or step-size. Basically, there are two ways in which quantization is carried out: uniform quantization and non-uniform quantization. ### Advantages of Uniform and Non-Uniform Quantization

 Uniform quantization Non-uniform quantization Increased accuracy of the discrete signals and high approximation Uniform spacing makes it easy to implement High signal-to-noise ratio (SNR) Low quantizer noise

## Quantization Errors

In some cases, the sampled analog value lies between two digital values or levels. In quantization, the sampled analog signal is represented by the digital value closer to the analog amplitude. This way of quantizing the signal introduces slight errors, called quantization errors.

As the step size decreases, the analog signal and the quantized values become closer. If the step size is more between two consecutive levels, the difference between the analog signal and the quantized discrete values becomes high, resulting in more quantization errors.

## Quantization Errors and Quantization Noise

When you want to convert analog signals to digital signals without loss, the quantization error is not favorable. When dealing with quantization error in sine waves, it appears as harmonics. The wideband noise in audio signals is mostly due to quantization error.

Quantization error is responsible for introducing noises into sample data systems. The quantization error and noise are dependent on the resolution of the analog to digital converters. As the resolution of the analog-to-digital conversion increases, the quantization errors and quantization noises decrease.