Quantization in Signal Processing:
– Quantization involves mapping input values to output values in a smaller set.
– Rounding and truncation are common quantization processes.
– Quantization is essential in digital signal processing and lossy compression.
– Quantization error is the difference between input and quantized values.
– An analog-to-digital converter is a type of quantizer.
– Quantization is a non-linear and irreversible process.
– Input values can be infinite and continuous, while output values are finite.
– Vector quantization applies quantization to multi-dimensional data.
– Quantization can have different resolutions and levels.
– Mid-tread and mid-riser quantization involve rounding and truncation.
– Mid-riser quantizers do not have a zero output value, while mid-tread quantizers have a zero output level.
– Analog-to-digital converter (ADC) involves sampling and quantization processes.
– Common word-lengths for quantization are 8-bit, 16-bit, and 24-bit.
Quantization Error and Noise:
– Additive noise model used for quantization error analysis.
– Deterministic relationship between quantization error and signal.
– Dithered quantization ensures independence of quantization error.
– Distortion caused by quantization error can be eliminated by dithering.
– Quantization error models for rounding and truncation.
– Relationship between quantization bits and signal-to-quantization-noise power ratio.
– Quantization error dependent on input signal at lower amplitudes.
– Quantization noise as a model of quantization error in ADC.
– Calculation of Signal-to-quantization-noise ratio (SQNR) for different signals.
– Influence of signal amplitude and frequency spectrum on quantization noise.
Quantization Design and Optimization:
– Granular distortion and overload distortion in quantizer design.
– Balancing granular distortion and overload distortion.
– Use of automatic gain control to control signal amplitude.
– Iterative optimization approaches for quantizer design.
– Neglecting the entropy constraint: Lloyd–Max quantization.
– Uniform quantization and the 6dB/bit approximation.
– Impact of setting the bit rate constraint to 0 on optimization problem.
– Reduction of optimization problem to distortion minimization.
– Lloyd–Max quantizer and its application for uniformly distributed input PDF.
– Step size calculation using the SQNR formula.
– 6dB improvement in SQNR for each extra bit used in quantization.
Quantization Applications and Strategies:
– Strategies to minimize quantization noise.
– Increasing the number of quantization levels reduces quantization error.
– Dithering techniques can help spread out the noise spectrum.
– Oversampling before quantization can improve resolution.
– Noise shaping algorithms shift noise to frequencies where it is less perceptible.
– Applications of understanding quantization noise.
– Crucial in designing audio and video compression algorithms.
– Essential for efficient data storage and transmission.
– Important in digital communication systems.
– Plays a key role in the performance of analog-to-digital converters.
Additional Concepts and Related Topics:
– Physical quantities in various fields are quantized by physical entities.
– Examples include electronics (electrons), optics (photons), biology (DNA), and physics (Planck limits).
– Limitations of quantization apply in chemistry (molecules).
– Quantum noise and quantum limit are relevant in these fields.
– Related concepts such as Beta encoder, color quantization, and data binning.
– Discretization, discretization error, and posterization in signal processing.
– Pulse-code modulation and quantization in image processing.
– Regression dilution as a bias caused by errors like quantization in variables.
– Quantile and JPEG 2000 Core Coding System as other relevant topics.
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. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.
The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer.
