Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. An analog-to-digital converter is an example of a quantizer.

To say that something is quantized means that we can obtain that quantity in multiples of a given amount of the quantity.

Although quantization may seem to be an unfamiliar concept, we encounter it frequently. For example, US money is integral multiples of pennies. Similarly, musical instruments like a piano or a trumpet can produce only certain musical notes, such as C or F sharp.

We simplify time into discrete numbers. Another example is capturing a digital image by representing each pixel by a certain number of bits, thereby reducing the continuous color spectrum of real life to discrete colors. Quantization, in essence, lessens the number of bits needed to represent information.

There are two types of Quantization – Uniform Quantization and Non-uniform Quantization. The type of quantization in which the quantization levels are uniformly spaced is termed as a Uniform Quantization.

Quantization is the process of mapping continuous amplitude (analog) signal into discrete amplitude (digital) signal. Each of these levels represents a fixed input amplitude. During quantization, the input amplitude is round off to the nearest quantized level. This rounding off is known as quantization error.

Quantization noise results when a continuous random variable is converted to a discrete one or when a discrete random variable is converted to one with fewer levels. In images, quantization noise often occurs in the acquisition process.

The process of oversampling to reduce ADC quantization noise is straightforward. An analog signal is digitized at an fs sample rate that is higher than the minimum rate needed to satisfy the Nyquist criterion (twice the input analog signal’s bandwidth) and then lowpass filtered.

Granular or Idle noise occurs when the step size is too large compared to small variation in the input signal. This means that for very small variations in the input signal, the staircase signal is changed by large amount (Δ) because of large step size.

Oversampling Description Oversampling is a cost-effective process of sampling the input signal at a much higher rate than the Nyquist frequency to increase the SNR and resolution (ENOB) that also relaxes the requirements on the antialiasing filter.

Random oversampling duplicates examples from the minority class in the training dataset and can result in overfitting for some models. Random undersampling deletes examples from the majority class and can result in losing information invaluable to a model.

Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements.

Aliasing occurs because signal frequencies can overlap if the sampling frequency is too low. Sometimes the highest frequency components of a signal are simply noise, or do not contain useful information. To prevent aliasing of these frequencies, we can filter out these components before sampling the signal.

Sampling rate (sometimes called sampling frequency or Fs) is the number of data points acquired per second. A sampling rate of 2000 samples/second means that 2000 discrete data points are acquired every second. The inverse of sampling frequency (Fs) is the sampling interval or Δt.

Sampling rate or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete or digital signal.