61-414: W800 , W 800 or W–800 may refer to: Sony Ericsson W800 , a mobile phone Kawasaki W800 , a motorbike [REDACTED] Topics referred to by the same term This disambiguation page lists articles associated with the same title formed as a letter–number combination. If an internal link led you here, you may wish to change the link to point directly to
122-476: A binary codeword c k {\displaystyle c_{k}} . An important consideration is the number of bits used for each codeword, denoted here by l e n g t h ( c k ) {\displaystyle \mathrm {length} (c_{k})} . As a result, the design of an M {\displaystyle M} -level quantizer and an associated set of codewords for communicating its index values requires finding
183-430: A dead-zone quantizer is given by where r k {\displaystyle r_{k}} is a reconstruction offset value in the range of 0 to 1 as a fraction of the step size. Ordinarily, 0 ≤ r k ≤ 1 2 {\displaystyle 0\leq r_{k}\leq {\tfrac {1}{2}}} when quantizing input data with a typical probability density function (PDF) that
244-485: A finite set of discrete values. Most commonly, these discrete values are represented as fixed-point words. Though any number of quantization levels is possible, common word-lengths are 8-bit (256 levels), 16-bit (65,536 levels) and 24-bit (16.8 million levels). Quantizing a sequence of numbers produces a sequence of quantization errors which is sometimes modeled as an additive random signal called quantization noise because of its stochastic behavior. The more levels
305-409: A mid-riser or mid-tread quantizer may not actually be a uniform quantizer – i.e., the size of the quantizer's classification intervals may not all be the same, or the spacing between its possible output values may not all be the same. The distinguishing characteristic of a mid-riser quantizer is that it has a classification threshold value that is exactly zero, and the distinguishing characteristic of
366-411: A mid-riser uniform quantizer is given by: where the classification rule is given by and the reconstruction rule is Note that mid-riser uniform quantizers do not have a zero output value – their minimum output magnitude is half the step size. In contrast, mid-tread quantizers do have a zero output level. For some applications, having a zero output signal representation may be a necessity. In general,
427-422: A mid-tread quantizer is that is it has a reconstruction value that is exactly zero. A dead-zone quantizer is a type of mid-tread quantizer with symmetric behavior around 0. The region around the zero output value of such a quantizer is referred to as the dead zone or deadband . The dead zone can sometimes serve the same purpose as a noise gate or squelch function. Especially for compression applications,
488-407: A percentage of the full signal range, changes by a factor of 2 for each 1-bit change in the number of quantization bits. The potential signal-to-quantization-noise power ratio therefore changes by 4, or 10 ⋅ log 10 ( 4 ) {\displaystyle \scriptstyle 10\cdot \log _{10}(4)} , approximately 6 dB per bit. At lower amplitudes
549-405: A quantizer is countable, any quantizer can be decomposed into two distinct stages, which can be referred to as the classification stage (or forward quantization stage) and the reconstruction stage (or inverse quantization stage), where the classification stage maps the input value to an integer quantization index k {\displaystyle k} and the reconstruction stage maps
610-452: A quantizer uses, the lower is its quantization noise power. Rate–distortion optimized quantization is encountered in source coding for lossy data compression algorithms, where the purpose is to manage distortion within the limits of the bit rate supported by a communication channel or storage medium. The analysis of quantization in this context involves studying the amount of data (typically measured in digits or bits or bit rate ) that
671-417: A rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input data. An analog-to-digital converter (ADC) can be modeled as two processes: sampling and quantization. Sampling converts a time-varying voltage signal into a discrete-time signal , a sequence of real numbers. Quantization replaces each real number with an approximation from
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#1732855663257732-413: A selected set of design constraints such as the bit rate R {\displaystyle R} and distortion D {\displaystyle D} . Assuming that an information source S {\displaystyle S} produces random variables X {\displaystyle X} with an associated PDF f ( x ) {\displaystyle f(x)} ,
793-604: 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
854-583: Is also MP3 and AAC compatible and has up to 30 hours playback time in Music mode. The standby and talktime the battery can support is 400 hours and 9 hours respectively. Whilst being a highly capable phone, it does suffer from some of the flaws that the K750 does. The primary concern is that of the joystick. This has long been a contentious issue with some reviewers finding it hard to use and highly susceptible to damage over time, in as much as it will cease to function (however,
915-564: Is assumed that distortion is measured by mean squared error, the distortion D , is given by: A key observation is that rate R {\displaystyle R} depends on the decision boundaries { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} and the codeword lengths { l e n g t h ( c k ) } k = 1 M {\displaystyle \{\mathrm {length} (c_{k})\}_{k=1}^{M}} , whereas
976-409: Is not always a valid assumption. Quantization error (for quantizers defined as described here) is deterministically related to the signal and not entirely independent of it. Thus, periodic signals can create periodic quantization noise. And in some cases it can even cause limit cycles to appear in digital signal processing systems. One way to ensure effective independence of the quantization error from
1037-498: Is planned, though end users have provided solutions that can be applied by directly accessing the phone's filesystem. A fake W800 was released in China under the name of Music Mobile W800c. It is similar in design to the SE W800 but is slightly taller. The Walkman logo on the bottom of the phone is flipped horizontally, 'Sony Ericsson' at the top of the phone is replaced by 'music mobile',
1098-579: Is symmetric around zero and reaches its peak value at zero (such as a Gaussian , Laplacian , or generalized Gaussian PDF). Although r k {\displaystyle r_{k}} may depend on k {\displaystyle k} in general, and can be chosen to fulfill the optimality condition described below, it is often simply set to a constant, such as 1 2 {\displaystyle {\tfrac {1}{2}}} . (Note that in this definition, y 0 = 0 {\displaystyle y_{0}=0} due to
1159-439: 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
1220-411: Is used to quantize, the quantization error has a mean of zero and the root mean square (RMS) value is the standard deviation of this distribution, given by 1 12 L S B ≈ 0.289 L S B {\displaystyle \scriptstyle {\frac {1}{\sqrt {12}}}\mathrm {LSB} \ \approx \ 0.289\,\mathrm {LSB} } . When truncation
1281-407: Is used to represent the output of the quantizer, and studying the loss of precision that is introduced by the quantization process (which is referred to as the distortion ). Most uniform quantizers for signed input data can be classified as being of one of two types: mid-riser and mid-tread . The terminology is based on what happens in the region around the value 0, and uses the analogy of viewing
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#17328556632571342-452: Is used, the error has a non-zero mean of 1 2 L S B {\displaystyle \scriptstyle {\frac {1}{2}}\mathrm {LSB} } and the RMS value is 1 3 L S B {\displaystyle \scriptstyle {\frac {1}{\sqrt {3}}}\mathrm {LSB} } . Although rounding yields less RMS error than truncation, the difference is only due to
1403-657: The Lagrange multiplier λ {\displaystyle \lambda } is a non-negative constant that establishes the appropriate balance between rate and distortion. Solving the unconstrained problem is equivalent to finding a point on the convex hull of the family of solutions to an equivalent constrained formulation of the problem. However, finding a solution – especially a closed-form solution – to any of these three problem formulations can be difficult. Solutions that do not require multi-dimensional iterative optimization techniques have been published for only three PDFs:
1464-764: The Nokia N91 , the Nokia 3250 , and the Samsung SGH-i300 and its successor the Samsung SGH-i310 are its main competitors. The Sony Ericsson W800 was replaced by the Sony Ericsson W700 in April 2006 replacing the size of the memory stick with a 256 MB and eliminating the camera's autofocus function thus reducing the cost of the handset. Also, it is available in a different case colour option called Titanium Gold, in addition to
1525-413: The 'Walkman' on the side is replaced by 'Musicvideo'. The fake phone has a 1.3 MP camera, FM radio and uses MicroSD cards. The phones software also copies some elements of the SE W800, the default wallpaper is the default Walkman image, the main menu uses Sony Ericsson icons (Walkman, PlayNow, Contacts etc.). Quantization noise Quantization , in mathematics and digital signal processing ,
1586-568: The UK), was the first Sony Ericsson phone to use the Walkman brand . The phone features Bluetooth v1.2 (with full Bluetooth 2.0 compliance), Infrared and USB connectivity. The W800 is very similar to the Sony Ericsson K750 but differs with regards to its media playback software and its cosmetic design changes. The major differences to the K750 are the included 512 MB Memory Stick PRO Duo ,
1647-538: The W800's Smooth White (burnt orange and cream). The W810 proceeded after the W800. The Sony Ericsson W700 comes included with a 256 MB Memory Stick Pro Duo instead of 512 MB . The W800 officially supports external memory capacity of only 2 GB, while its successor the W810 supports 4 GB. The key feature of this cellphone is the 2-megapixel camera with autofocus, video recording function, and flash. The phone
1708-459: The W810i resolves this issue). The other is that the construction quality, whilst physically solid, is prone to creaking and wear over time. The screen, again whilst of a good out of the box quality, is prone to fingerprints and scratching because it is mounted flush within the phone, meaning if left to rest face down damage can occur. The dust gets trapped inside the screen easily and reduces visibility of
1769-439: The appropriate balance is the use of automatic gain control (AGC). However, in some quantizer designs, the concepts of granular error and overload error may not apply (e.g., for a quantizer with a limited range of input data or with a countably infinite set of selectable output values). A scalar quantizer, which performs a quantization operation, can ordinarily be decomposed into two stages: These two stages together comprise
1830-434: 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. For example, rounding a real number x {\displaystyle x} to
1891-443: The dead-zone may be given a different width than that for the other steps. For an otherwise-uniform quantizer, the dead-zone width can be set to any value w {\displaystyle w} by using the forward quantization rule where the function sgn {\displaystyle \operatorname {sgn} } ( ) is the sign function (also known as the signum function). The general reconstruction rule for such
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1952-407: The dead-zone quantizer is also a uniform quantizer, since the central dead-zone of this quantizer has the same width as all of its other steps, and all of its reconstruction values are equally spaced as well. A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of additive white noise – having negligible correlation with
2013-571: The definition of the sgn {\displaystyle \operatorname {sgn} } ( ) function, so r 0 {\displaystyle r_{0}} has no effect.) A very commonly used special case (e.g., the scheme typically used in financial accounting and elementary mathematics) is to set w = Δ {\displaystyle w=\Delta } and r k = 1 2 {\displaystyle r_{k}={\tfrac {1}{2}}} for all k {\displaystyle k} . In this case,
2074-399: The design and analysis of quantization behavior, and it illustrates how the quantized data can be communicated over a communication channel – a source encoder can perform the forward quantization stage and send the index information through a communication channel, and a decoder can perform the reconstruction stage to produce the output approximation of the original input data. In general,
2135-451: The display. However these factors have not stopped it becoming highly popular. Also the phone has been found to randomly restart and turn off, especially while coming out of the clock on sleep mode. Some users experience a high level of background hiss and quantization noise when using the Walkman feature at low volume levels, a problem that first appeared in a firmware update. No official fix
2196-435: The distortion D {\displaystyle D} depends on the decision boundaries { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} and the reconstruction levels { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} . After defining these two performance metrics for
2257-455: The distortion. Quantization noise is a model of quantization error introduced by quantization in the ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent. It can be modelled in several different ways. In an ideal ADC, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and
2318-426: The exact amplitude of the signal. The calculations are relative to full-scale input. For smaller signals, the relative quantization distortion can be very large. To circumvent this issue, analog companding can be used, but this can introduce distortion. Often the design of a quantizer involves supporting only a limited range of possible output values and performing clipping to limit the output to this range whenever
2379-412: The forward quantization stage may use any function that maps the input data to the integer space of the quantization index data, and the inverse quantization stage can conceptually (or literally) be a table look-up operation to map each quantization index to a corresponding reconstruction value. This two-stage decomposition applies equally well to vector as well as scalar quantizers. Because quantization
2440-408: The index k {\displaystyle k} to the reconstruction value y k {\displaystyle y_{k}} that is the output approximation of the input value. For the example uniform quantizer described above, the forward quantization stage can be expressed as and the reconstruction stage for this example quantizer is simply This decomposition is useful for
2501-428: The input exceeds the supported range. The error introduced by this clipping is referred to as overload distortion. Within the extreme limits of the supported range, the amount of spacing between the selectable output values of a quantizer is referred to as its granularity , and the error introduced by this spacing is referred to as granular distortion. It is common for the design of a quantizer to involve determining
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2562-461: The input signal is a full-amplitude sine wave the distribution of the signal is no longer uniform, and the corresponding equation is instead Here, the quantization noise is once again assumed to be uniformly distributed. When the input signal has a high amplitude and a wide frequency spectrum this is the case. In this case a 16-bit ADC has a maximum signal-to-noise ratio of 98.09 dB. The 1.761 difference in signal-to-noise only occurs due to
2623-487: The input-output function of the quantizer as a stairway . Mid-tread quantizers have a zero-valued reconstruction level (corresponding to a tread of a stairway), while mid-riser quantizers have a zero-valued classification threshold (corresponding to a riser of a stairway). Mid-tread quantization involves rounding. The formulas for mid-tread uniform quantization are provided in the previous section. Mid-riser quantization involves truncation. The input-output formula for
2684-416: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=W800&oldid=933240670 " Category : Letter–number combination disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Sony Ericsson W800 The W800 Walkman , released in 2005 (1 August 2005 in
2745-522: The introduction of the Flight mode function where all radio signals are switched off, and the stereo portable handsfree headset Sony Ericsson HPM-70 , which features a 3.5 mm headphone jack , allowing the included headphones to be swapped for any other pair of headphones which has a 3.5 mm headphone jack. The Motorola ROKR E1 iTunes -enabled mobile phone, its successor the Motorola ROKR E2 ,
2806-415: The mathematical operation of y = Q ( x ) {\displaystyle y=Q(x)} . Entropy coding techniques can be applied to communicate the quantization indices from a source encoder that performs the classification stage to a decoder that performs the reconstruction stage. One way to do this is to associate each quantization index k {\displaystyle k} with
2867-418: The nearest integer value forms a very basic type of quantizer – a uniform one. A typical ( mid-tread ) uniform quantizer with a quantization step size equal to some value Δ {\displaystyle \Delta } can be expressed as where the notation ⌊ ⌋ {\displaystyle \lfloor \ \rfloor } denotes the floor function . Alternatively,
2928-413: The nearest integer, the step size Δ {\displaystyle \Delta } is equal to 1. With Δ = 1 {\displaystyle \Delta =1} or with Δ {\displaystyle \Delta } equal to any other integer value, this quantizer has real-valued inputs and integer-valued outputs. When the quantization step size (Δ) is small relative to
2989-427: The noise power by the factor 1 / 4 . In terms of decibels , the noise power change is 10 ⋅ log 10 ( 1 / 4 ) ≈ − 6 d B . {\displaystyle \scriptstyle 10\cdot \log _{10}(1/4)\ \approx \ -6\ \mathrm {dB} .} Because the set of possible output values of
3050-399: The probability p k {\displaystyle p_{k}} that the random variable falls within a particular quantization interval I k {\displaystyle I_{k}} is given by: The resulting bit rate R {\displaystyle R} , in units of average bits per quantized value, for this quantizer can be derived as follows: If it
3111-415: The proper balance between granular distortion and overload distortion. For a given supported number of possible output values, reducing the average granular distortion may involve increasing the average overload distortion, and vice versa. A technique for controlling the amplitude of the signal (or, equivalently, the quantization step size Δ {\displaystyle \Delta } ) to achieve
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#17328556632573172-449: The quantization error becomes dependent on the input signal, resulting in distortion. This distortion is created after the anti-aliasing filter, and if these distortions are above 1/2 the sample rate they will alias back into the band of interest. In order to make the quantization error independent of the input signal, the signal is dithered by adding noise to the signal. This slightly reduces signal to noise ratio, but can completely eliminate
3233-427: The quantizer, a typical rate–distortion formulation for a quantizer design problem can be expressed in one of two ways: Often the solution to these problems can be equivalently (or approximately) expressed and solved by converting the formulation to the unconstrained problem min { D + λ ⋅ R } {\displaystyle \min \left\{D+\lambda \cdot R\right\}} where
3294-468: The same quantizer may be expressed in terms of the ceiling function , as (The notation ⌈ ⌉ {\displaystyle \lceil \ \rceil } denotes the ceiling function). The essential property of a quantizer is having a countable-set of possible output-values members smaller than the set of possible input values. The members of the set of output values may have integer, rational, or real values. For simple rounding to
3355-454: The signal and an approximately flat power spectral density . The additive noise model is commonly used for the analysis of quantization error effects in digital filtering systems, and it can be very useful in such analysis. It has been shown to be a valid model in cases of high-resolution quantization (small Δ {\displaystyle \Delta } relative to the signal strength) with smooth PDFs. Additive noise behavior
3416-399: The signal being a full-scale sine wave instead of a triangle or sawtooth. For complex signals in high-resolution ADCs this is an accurate model. For low-resolution ADCs, low-level signals in high-resolution ADCs, and for simple waveforms the quantization noise is not uniformly distributed, making this model inaccurate. In these cases the quantization noise distribution is strongly affected by
3477-480: The signal has a uniform distribution covering all quantization levels, the Signal-to-quantization-noise ratio (SQNR) can be calculated from where Q is the number of quantization bits. The most common test signals that fulfill this are full amplitude triangle waves and sawtooth waves . For example, a 16-bit ADC has a maximum signal-to-quantization-noise ratio of 6.02 × 16 = 96.3 dB. When
3538-444: The source signal is to perform dithered quantization (sometimes with noise shaping ), which involves adding random (or pseudo-random ) noise to the signal prior to quantization. In the typical case, the original signal is much larger than one least significant bit (LSB). When this is the case, the quantization error is not significantly correlated with the signal, and has an approximately uniform distribution . When rounding
3599-500: The static (DC) term of 1 2 L S B {\displaystyle \scriptstyle {\frac {1}{2}}\mathrm {LSB} } . The RMS values of the AC error are exactly the same in both cases, so there is no special advantage of rounding over truncation in situations where the DC term of the error can be ignored (such as in AC coupled systems). In either case, the standard deviation, as
3660-419: The values of { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} , { c k } k = 1 M {\displaystyle \{c_{k}\}_{k=1}^{M}} and { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} which optimally satisfy
3721-404: The variation in the signal being quantized, it is relatively simple to show that the mean squared error produced by such a rounding operation will be approximately Δ 2 / 12 {\displaystyle \Delta ^{2}/12} . Mean squared error is also called the quantization noise power . Adding one bit to the quantizer halves the value of Δ, which reduces
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