Quantization Error In Multimedia
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and the difference between the original signal and the reconstructed signal (red). The quantization error definition difference between the original signal and the reconstructed signal is the quantization error quantization error formula and, in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal quantization error in pcm processing, is the process of mapping a large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in how to reduce quantization error 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
Quantization Error Example
an example of a quantizer. Contents 1 Basic properties of quantization 2 Basic types of quantization 2.1 Analog-to-digital converter (ADC) 2.2 Rate–distortion optimization 3 Rounding example 4 Mid-riser and mid-tread uniform quantizers 5 Dead-zone quantizers 6 Granular distortion and overload distortion 7 The additive noise model for quantization error 8 Quantization error models 9 Quantization noise model 10 Rate–distortion quantizer design 11 Neglecting the entropy constraint: Lloyd–Max quantization 12 Uniform quantization and the 6 dB/bit approximation 13 Other fields 14 See also 15 Notes 16 References 17 External links Basic properties of quantization[edit] Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible in general to recover the exact input value when given only the output value). The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be finite or countably infinite. The input and output sets involved in quantization can be defined in a
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Uniform Quantization
Nyquist Sampling Rate Quantization Unit Conversion Explore More Learn It! Analog and quantization error in analog to digital conversion Digital SignalsDigital signals are more resilient against noise than analog signals. An analog signal exists throughout a continuous interval of what is quantization time and/or takes on a continuous range of values. A sinusoidal signal (also called a pure tone in acoustics) has both of these properties. Figure 1 Fig. 1: Analog signal. This https://en.wikipedia.org/wiki/Quantization_(signal_processing) signal $v(t)=\cos(2\pi ft)$ could be a perfect analog recording of a pure tone of frequency $f$ Hz. If $f=440 \text{ Hz}$, this tone is the musical note $A$ above middle $C$, to which orchestras often tune their instruments. The period $T=1/f$ is the duration of one full oscillation. In reality, electrical recordings suffer from noise that unavoidably degrades the signal. The more a recording https://courses.engr.illinois.edu/ece110/fa2016/content/courseNotes/files/?samplingAndQuantization is transferred from one analog format to another, the more it loses fidelity to the original.
Figure 2 Fig. 2: Noisy analog signal. Noise degrades the sinusoidal signal in Fig. 1. It is often impossible to recover the original signal exactly from the noisy version. A digital signal is a sequence of discrete symbols. If these symbols are zeros and ones, we call them bits. As such, a digital signal is neither continuous in time nor continuous in its range of values. and, therefore, cannot perfectly represent arbitrary analog signals. On the other hand, digital signals are resilient against noise. Figure 3 Fig. 3: Analog transmission of a digital signal. Consider a digital signal $100110$ converted to an analog signal for radio transmission. The received signal suffers from noise, but given sufficient bit duration $T_b$, it is still easy to read off the original sequence $100110$ perfectly. Digital signals can be stored on digital media (like a compact disc) and manipulated on digital systems (like the integrated circuit in a CD player). This digital technology enables a variety of digital processing unavailable to analog systems. For example, the music signDelta Modulation (DM) QUANTIZATION NOISE Adaptive Delta Modulation Coding Speech at Low Bit Rates Digital Multiplexers Light Wave Transmission Quantization Process The process of transforming Sampled http://www.allsyllabus.com/aj/note/ECE/Digital%20Communication/unit3/Quantization%20Process.php amplitude values of a message signal into a discrete amplitude value is referred to as Quantization. The quantization Process has a two-fold effect: 1. the peak-to-peak range of the input sample values is subdivided into a finite set of decision levels or decision thresholds that are aligned with the risers of the staircase, and 2. the output is assigned a discrete value selected from a finite quantization error set of representation levels that are aligned with the treads of the staircase.. A quantizer is memory less in that the quantizer output is determined only by the value of a corresponding input sample, independently of earlier analog samples applied to the input. Types of Quantizers: 1. Uniform Quantizer 2. Non- Uniform Quantizer 0 Ts 2Ts 3Ts Time Analog Signal Discrete Samples ( Quantized ) In Uniform quantization error in type, the quantization levels are uniformly spaced, whereas in nonuniform type the spacing between the levels will be unequal and mostly the relation is logarithmic. Types of Uniform Quantizers: ( based on I/P - O/P Characteristics) 1. Mid-Rise type Quantizer 2. Mid-Tread type Quantizer In the stair case like graph, the origin lies the middle of the tread portion in Mid –Tread type where as the origin lies in the middle of the rise portion in the Mid-Rise type. Mid – tread type: Quantization levels – odd number. Mid – Rise type: Quantization levels – even number. Quantization Noise and Signal-to-Noise: “The Quantization process introduces an error defined as the difference between the input signal, x(t) and the output signal, yt). This error is called the Quantization Noise.” q(t) = x(t) – y(t) Quantization noise is produced in the transmitter end of a PCM system by rounding off sample values of an analog base-band signal to the nearest permissible representation levels of the quantizer. As such quantization noise differs from channel noise in that it is signal dependent. Let ‘Δ’ be the step size of a quantizer and L be the total number of quantization levels. Quantization levels ar