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| {{for|"signal-to-noise ratio" in statistics|Cohen's d}}
| | Burn off fat: this will depend! Several newcomers benefit simply because they could burn calories by performing a lengthier cardio routine relative to a weight training regimen which will weakness them faster from performing cardio before weight training exercise. However, if you should be sophisticated within your workout routine, you can do a series of strength training followed closely by cardio to assist increase fat loss on account of an accelerated discharge of essential fatty acids and HGH to the system.<br><br>I suggest all police fitness be based around a hiit software (High Intensity Circuit Training). hiit is just a type of teaching that intersperses brief times of powerful physical exercise with brief (or smaller) bouts of sleep and recovery. hiit training may be tailored to many kinds of workout including strolling, biking, bodyweight calisthenics, string missing, striking huge carrier, etc. Types can differ, but the fundamental premise is still exactly the same - perform a quick warm up, accompanied by multiple fights of intensive [http://Thesaurus.com/browse/workout+spaced workout spaced] with equal or near equal times of relaxation, followed closely by a short cool down.<br><br>Making the decision to lose weight is not pretty difficult, and having this gear will surely encourage one to follow-up on any workout. You can find different varieties of stationary bicycles obtainable in industry nowadays, therefore looking for the right choice for you is actually a large problem. You can start of by going to gear evaluation sites and different Web fitness boards to examine and assess their rates and different models. There are always a large amount of aspects to influence your purchase. Howmuch have you been ready to spend for your motorcycle? Are you prepared to save money for the fancy settings and patterns?<br><br>Your Results - You'll burn to 300 calories depending exactly how many tracks you conduct in 15 minutes. Plus you'll continue to burn calories long. After your done review that to some 60 minute onslaught to the treadmill which only burn off fat for 4-6 hours. If you dislike the treadmill these circuits would be the easiest way to get rid of fat quickly. This Full body routine will keep your heartrate raised by jumping jacks and using exercises.<br><br>Incorporate whole food diet ([https://www.flickr.com/people/126230156@N07/ https://www.flickr.com/people/126230156@N07/]) (HIIT) into your cardio [http://Www.Wonderhowto.com/search/workouts/ workouts]. By now you are probably not unaware that cardio is really a necessity in a weightloss program. Being a standard concept, you need to do your cardio in a moderate-intensity charge 5-6 times for 45-60 minutes at a time. To stop on your calorie expenditure up a step, change 2 of your cardio sessions during the week with intensive training. If you should be a treadmill walker, try then, and to raise the slope to some sharp walk every fifth minute continue walking on the level plane. If you should be a runner, try incorporating quartermile chips after every distance at 80-90% of your perceived pace of exercise.<br><br>Recovery Hierarchy: Keep a group race interval and progressively decrease the restoration time by 10 seconds before only 10 seconds relax. And soon you are back again to your place then increase the sleep time by 10 seconds per span,. |
| {{Redirect|Signal to noise||Signal to Noise (disambiguation)}}
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| {{Antennas|Characteristics}}
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| '''Signal-to-noise ratio''' (often abbreviated '''SNR''' or '''S/N''') is a measure used in science and engineering that compares the level of a desired [[Signal (electrical engineering)|signal]] to the level of background [[noise]]. It is defined as the ratio of signal power to the noise power, often expressed in [[decibel]]s. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any form of signal (such as isotope levels in an [[ice core]] or [[biochemical signaling]] between cells).
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| The signal-to-noise ratio, the [[Bandwidth (signal processing)|bandwidth]], and the [[channel capacity]] of a [[Channel (communications)|communication channel]] are connected by the [[Shannon–Hartley theorem]].
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| Signal-to-noise ratio is sometimes used informally to refer to the ratio of useful [[information]] to false or irrelevant data in a conversation or exchange. For example, in [[internet forum|online discussion forums]] and other online communities, [[off-topic]] posts and [[spamming|spam]] are regarded as "noise" that interferes with the "signal" of appropriate discussion.
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| ==Definition==
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| Signal-to-noise ratio is defined as the [[power (physics)|power]] ratio between a [[signal (information theory)|signal]] (meaningful information) and the background [[noise (electronic)|noise]] (unwanted signal):
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| :<math>
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| \mathrm{SNR} = \frac{P_\mathrm{signal}}{P_\mathrm{noise}},
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| </math>
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| where ''P'' is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system [[bandwidth (signal processing)|bandwidth]].
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| If the variance of the signal and noise are known, and the signal is zero-mean:<ref>http://www.scholarpedia.org/article/Signal-to-noise_ratio</ref>
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| :<math>
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| \mathrm{SNR} = \frac{\sigma^2_\mathrm{signal}}{\sigma^2_\mathrm{noise}}.
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| </math>
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| If the signal and the noise are measured across the same [[Electrical impedance|impedance]], then the SNR can be obtained by calculating the square of the [[amplitude]] ratio:
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| :<math>
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| \mathrm{SNR} = \frac{P_\mathrm{signal}}{P_\mathrm{noise}} = \left ( \frac{A_\mathrm{signal}}{A_\mathrm{noise} } \right )^2,
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| </math>
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| where ''A'' is [[root mean square]] (RMS) [[amplitude]] (for example, RMS voltage). Because many signals have a very wide [[dynamic range]], SNRs are often expressed using the [[logarithm]]ic [[decibel]] scale. In decibels, the SNR is defined as
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| :<math>
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| \mathrm{SNR_{dB}} = 10 \log_{10} \left ( \frac{P_\mathrm{signal}}{P_\mathrm{noise}} \right ) = {P_\mathrm{signal,dB} - P_\mathrm{noise,dB}},
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| </math>
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| which may equivalently be written using amplitude ratios as
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| :<math>
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| \mathrm{SNR_{dB}} = 10 \log_{10} \left ( \frac{A_\mathrm{signal}}{A_\mathrm{noise}} \right )^2 = 20 \log_{10} \left ( \frac{A_\mathrm{signal}}{A_\mathrm{noise}} \right ).
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| </math>
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| The concepts of signal-to-noise ratio and dynamic range are closely related. Dynamic range measures the ratio between the strongest un-[[distortion|distorted]] signal on a [[channel (communications)|channel]] and the minimum discernable signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level (not necessarily the most powerful signal possible) and noise. Measuring signal-to-noise ratios requires the selection of a representative or ''reference'' signal. In [[audio engineering]], the reference signal is usually a [[sine wave]] at a standardized [[nominal level|nominal]] or [[alignment level]], such as 1 kHz at +4 [[dBu]] (1.228 V<sub>RMS</sub>).
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| SNR is usually taken to indicate an ''average'' signal-to-noise ratio, as it is possible that (near) instantaneous signal-to-noise ratios will be considerably different. The concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'.
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| {{#tag:ref|The connection between [[optical power]] and [[voltage]] in an imaging system is linear. This usually means that the SNR of the electrical signal is calculated by the ''10 log'' rule. With an [[interferometer|interferometric]] system, however, where interest lies in the signal from one arm only, the field of the electromagnetic wave is proportional to the voltage (assuming that the intensity in the second, the reference arm is constant). Therefore the optical power of the measurement arm is directly proportional to the electrical power and electrical signals from optical interferometry are following the [[20 log rule|''20 log'' rule]].<ref>Michael A. Choma, Marinko V. Sarunic, Changhuei Yang, Joseph A. Izatt. Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Optics Express, 11(18). Sept 2003.</ref>|group="note"}}
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| ==Difference from conventional power ==
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| In Physics, the average [[power (physics)|power]] of an AC signal is defined as the average value of voltage times current; for [[resistive]] (non-[[reactance (electronics)|reactive]]) circuits, where voltage and current are in phase, this is equivalent to the product of the [[root mean square|rms]] voltage and current:
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| :<math> \mathrm{P} = V_\mathrm{rms}I_\mathrm{rms}
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| </math>
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| :<math>
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| \mathrm{P}= \frac{V_\mathrm{rms}^{2}}{R} = I_\mathrm{rms}^{2} R
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| </math>
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| But in signal processing and communication, one usually assumes that <math>R=1 \Omega</math> so that factor is usually not included while measuring power or energy of a signal. This may cause some confusion among readers, but the resistance factor is not significant for typical operations performed in signal processing, or for computing power ratios. For most cases, the power of a signal would be considered to be simply
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| :<math>
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| \mathrm{P}= V_\mathrm{rms}^{2} = \frac{A^{2}}{2}
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| </math>
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| where 'A' is the amplitude of the AC signal.
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| ==Alternative definition==
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| An alternative definition of SNR is as the reciprocal of the [[coefficient of variation]], i.e., the ratio of [[mean]] to [[standard deviation]] of a signal or measurement:<ref>
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| {{cite book | title = Astronomical optics | author = D. J. Schroeder | edition = 2nd | publisher = Academic Press | year = 1999 | isbn = 978-0-12-629810-9 | page = 433 | url = http://books.google.com/books?id=v7E25646wz0C&pg=PA433}}</ref><ref name=b1>Bushberg, J. T., et al., ''[http://books.google.com/books?id=VZvqqaQ5DvoC&lpg=PA280 The Essential Physics of Medical Imaging,]'' (2e). Philadelphia: Lippincott Williams & Wilkins, 2006, p. 280.</ref>
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| :<math>
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| \mathrm{SNR} = \frac{\mu}{\sigma}
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| </math>
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| where <math>\mu</math> is the signal mean or [[expected value]] and <math>\sigma</math> is the standard deviation of the noise, or an estimate thereof.<ref group="note">The exact methods may vary between fields. For example, if the signal data are known to be constant, then <math>\sigma</math> can be calculated using the standard deviation of the signal. If the signal data are not constant, then <math>\sigma</math> can be calculated from data where the signal is zero or relatively constant.</ref> Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and [[luminance]]). Thus it is commonly used in [[image processing]],<ref>{{cite book|url=http://books.google.com/books?id=8uGOnjRGEzoC&lpg=PA354|title=Digital image processing|page=354|author=Rafael C. González, Richard Eugene Woods|publisher=Prentice Hall|year=2008|isbn=0-13-168728-X}}</ref><ref>{{cite book|url=http://books.google.com/books?id=VmvY4MTMFTwC&lpg=PA471|title=Image fusion: algorithms and applications|page=471|author=Tania Stathaki|publisher=Academic Press|year=2008|isbn=0-12-372529-1}}</ref><ref>{{cite book|url=http://books.google.com/books?id=7s8xpR-5rOUC&lpg=PA471 |title=Multi-Sensor Data Fusion: Theory and Practice|page=|author=Jitendra R. Raol|publisher=CRC Press|year=2009|isbn=1-4398-0003-0}}</ref><ref>{{cite book|url=http://books.google.com/books?id=Vs2AM2cWl1AC&lpg=PA26 |title=The image processing handbook|page=|author=John C. Russ|publisher=CRC Press|year=2007|isbn=0-8493-7254-2}}</ref> where the SNR of an [[image]] is usually calculated as the ratio of the [[mean]] pixel value to the [[standard deviation]] of the pixel values over a given neighborhood. Sometimes SNR is defined as the square of the alternative definition above.
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| The ''Rose criterion'' (named after [[Albert Rose (physicist)|Albert Rose]]) states that an SNR of at least 5 is needed to be able to distinguish image features at 100% certainty. An SNR less than 5 means less than 100% certainty in identifying image details.<ref name=b1/>
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| Yet another alternative, very specific and distinct definition of SNR is employed to characterize [[film speed|sensitivity]] of imaging systems; see [[Signal-to-noise ratio (imaging)]].
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| Related measures are the "[[contrast ratio]]" and the "[[contrast-to-noise ratio]]".
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| ==SNR for various modulation systems==
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| ===Amplitude modulation===
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| Channel signal-to-noise ratio is given by
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| :<math>\mathrm{(SNR)_{C,AM}} = \frac{A_c^2 (1 + k_a^2 P)} {2 W N_0}
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| </math>
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| where W is the bandwidth and <math>k_a</math> is modulation index
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| Output signal-to-noise ratio (of AM receiver) is given by
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| :<math>\mathrm{(SNR)_{O,AM}} = \frac{A_c^2 k_a^2 P} {2 W N_0}
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| </math>
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| ===Frequency modulation===
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| Channel signal-to-noise ratio is given by
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| :<math>\mathrm{(SNR)_{C,FM}} = \frac{A_c^2} {2 W N_0}
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| </math>
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| Output signal-to-noise ratio is given by
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| :<math>\mathrm{(SNR)_{O,FM}} = \frac{A_c^2 k_f^2 P} {2 N_0 W^3}
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| </math>
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| ==Improving SNR in practice==
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| [[Image:Analyse thermo gravimetrique bruit.png|thumb|Recording of the noise of a [[thermogravimetric analysis]] device that is poorly isolated from a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night.]]
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| All real measurements are disturbed by noise. This includes electronic noise, but can also include external events that affect the measured phenomenon — wind, vibrations, gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device. It is often possible to reduce the noise by controlling the environment. Otherwise, when the characteristics of the noise are known and are different from the signals, it is possible to [[filter (signal processing)|filter]] it or to process the signal.
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| For example, it is sometimes possible to use a [[lock-in amplifier]] to modulate and confine the signal within a very narrow bandwidth and then filter the detected signal to the narrow band where it resides, thereby eliminating most of the broadband noise. When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by averaging the measurement. In this case the noise goes down as the square root of the number of averaged samples.
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| ==Digital signals==
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| When a measurement is digitized, the number of bits used to represent the measurement determines the maximum possible signal-to-noise ratio. This is because the minimum possible [[noise]] level is the [[error]] caused by the [[quantization (signal processing)|quantization]] of the signal, sometimes called [[Quantization noise]]. This noise level is non-linear and signal-dependent; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization ("additive noise").
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| This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal's noise may be larger than the quantization noise. Real [[analog-to-digital converter]]s also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of [[dither]].
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| Although noise levels in a digital system can be expressed using SNR, it is more common to use [[Eb/N0|E<sub>b</sub>/N<sub>o</sub>]], the energy per bit per noise power spectral density.
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| The [[modulation error ratio]] (MER) is a measure of the SNR in a digitally modulated signal.
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| ===Fixed point===
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| {{see also|Fixed point arithmetic}}
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| For ''n''-bit integers with equal distance between quantization levels ([[quantization (signal processing)|uniform quantization]]) the [[dynamic range]] (DR) is also determined.
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| Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2<sup>''n''</sup>/1. The formula is then:
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| :<math>
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| \mathrm{DR_{dB}} = \mathrm{SNR_{dB}} = 20 \log_{10}(2^n) \approx 6.02 \cdot n
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| </math>
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| This relationship is the origin of statements like "[[16-bit]] audio has a dynamic range of 96 dB". Each extra quantization bit increases the dynamic range by roughly 6 dB.
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| Assuming a [[full-scale]] [[sine wave]] signal (that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal), the quantization noise approximates a [[sawtooth wave]] with peak-to-peak amplitude of one quantization level<ref name="maxim 728">[http://www.maxim-ic.com/appnotes.cfm/appnote_number/728 Defining and Testing Dynamic Parameters in High-Speed ADCs] — [[Maxim Integrated Products]] Application note 728</ref> and uniform distribution. In this case, the SNR is approximately
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| :<math>
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| \mathrm{SNR_{dB}} \approx 20 \log_{10} (2^n \sqrt {3/2}) \approx 6.02 \cdot n + 1.761
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| </math>
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| ===Floating point===
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| [[Floating point|Floating-point]] numbers provide a way to trade off signal-to-noise ratio for an increase in dynamic range. For n bit floating-point numbers, with n-m bits in the [[logarithm|mantissa]] and m bits in the [[exponent]]:
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| :<math>
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| \mathrm{DR_{dB}} = 6.02 \cdot 2^m
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| </math>
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| :<math>
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| \mathrm{SNR_{dB}} = 6.02 \cdot (n-m)
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| </math>
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| Note that the dynamic range is much larger than fixed-point, but at a cost of a worse signal-to-noise ratio. This makes floating-point preferable in situations where the dynamic range is large or unpredictable. Fixed-point's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6.02m. The very large dynamic range of floating-point can be a disadvantage, since it requires more forethought in designing algorithms.<ref name="rane fixed vs floating">[http://web.archive.org/web/20060515074349/http://www.rane.com/note153.html Fixed-Point vs. Floating-Point DSP for Superior Audio] — [[Rane Corporation]] technical library</ref>
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| <ref group="note">Often special filters are used to weight the noise: DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601; for video, special filters such as [[comb filter]]s may be used.</ref>
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| <ref group="note">Maximum possible full scale signal can be charged as peak-to-peak or as RMS. Audio uses RMS, Video P-P, which gave +9 dB more SNR for video.</ref>
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| ==Optical SNR==
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| Optical signals have a carrier frequency that is much higher than the modulation frequency (about 200 THz and more). This way the noise covers a bandwidth that is much wider than the signal itself. The resulting signal influence relies mainly on the filtering of the noise. To describe the signal quality without taking the receiver into account, the optical SNR (OSNR) is used. The OSNR is the ratio between the signal power and the noise power in a given bandwidth. Most commonly a reference bandwidth of 0.1 nm is used. This bandwidth is independent of the modulation format, the frequency and the receiver. For instance an OSNR of 20dB/0.1 nm could be given, even the signal of 40 GBit [[DPSK#Differential phase-shift keying (DPSK)|DPSK]] would not fit in this bandwidth. OSNR is measured with an [[optical spectrum analyzer]].
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| ==See also==
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| {{colbegin|2}}
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| * [[Audio system measurements]]
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| * [[Generation loss]]
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| * [[Near-far problem]]
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| * [[Noise margin]]
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| * [[Peak signal-to-noise ratio]]
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| * [[Signal-to-noise statistic]]
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| * [[SINR|Signal-to-noise-plus-interference ratio]]
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| * [[Signal to noise ratio (imaging)]]
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| * [[SINAD]]
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| * [[Subjective video quality]]
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| * [[Total harmonic distortion]]
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| * [[Video quality]]
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| {{colend}}
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| ==Notes==
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| {{Reflist|group="note"|1}}
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| ==References==
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| {{Reflist|2}}
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| ==External links==
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| * Taking the Mystery out of the Infamous Formula,"SNR = 6.02N + 1.76dB," and Why You Should Care. [http://www.analog.com/static/imported-files/tutorials/MT-001.pdf] Analog Devices
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| * [http://www.maxim-ic.com/appnotes.cfm/appnote_number/641 ADC and DAC Glossary] – [[Maxim Integrated Products]]
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| * [http://www.analog.com/static/imported-files/tutorials/MT-003.pdf Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you don't get lost in the noise floor] – [[Analog Devices]]
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| * [http://www.techonline.com/community/related_content/20771 The Relationship of dynamic range to data word size in digital audio processing]
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| * [http://www.sengpielaudio.com/calculator-noise.htm Calculation of signal-to-noise ratio, noise voltage, and noise level]
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| * [http://www.vias.org/simulations/simusoft_spectaccu.html Learning by simulations – a simulation showing the improvement of the SNR by time averaging]
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| * [http://focus.ti.com/lit/an/sbaa055/sbaa055.pdf Dynamic Performance Testing of Digital Audio D/A Converters]
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| * [http://www.circuitdesign.info/blog/2008/11/fundamentals-of-analogrf-design-noise-signal-power/ Fundamental theorem of analog circuits: a minimum level of power must be dissipated to maintain a level of SNR]
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| {{Noise}}
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| [[Category:Engineering ratios]]
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| [[Category:Error measures]]
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| [[Category:Measurement]]
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| [[Category:Noise]]
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| [[Category:Statistical ratios]]
| |
Burn off fat: this will depend! Several newcomers benefit simply because they could burn calories by performing a lengthier cardio routine relative to a weight training regimen which will weakness them faster from performing cardio before weight training exercise. However, if you should be sophisticated within your workout routine, you can do a series of strength training followed closely by cardio to assist increase fat loss on account of an accelerated discharge of essential fatty acids and HGH to the system.
I suggest all police fitness be based around a hiit software (High Intensity Circuit Training). hiit is just a type of teaching that intersperses brief times of powerful physical exercise with brief (or smaller) bouts of sleep and recovery. hiit training may be tailored to many kinds of workout including strolling, biking, bodyweight calisthenics, string missing, striking huge carrier, etc. Types can differ, but the fundamental premise is still exactly the same - perform a quick warm up, accompanied by multiple fights of intensive workout spaced with equal or near equal times of relaxation, followed closely by a short cool down.
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