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50-427: THD may refer to: Total harmonic distortion , a measure of the distortion of an audio signal Total Hi Def (Total HD), an optical disc format Th.D. or D.Th. or D.Theol., a Doctor of Theology degree Thames Ditton railway station , Surrey, National Rail station code THD Electronics , a guitar amplifier manufacturer Transanal hemorrhoidal dearterialization ,

100-408: A change of x percent in a quantity results in a final amount that is 100 +  x percent of the original amount (equivalently, (1 + 0.01 x ) times the original amount). Percent changes applied sequentially do not add up in the usual way. For example, if the 10% increase in price considered earlier (on the $ 200 item, raising its price to $ 220) is followed by a 10% decrease in

150-449: A denominator of 100 became increasingly standard, such that from the late 15th century to the early 16th century, it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three . By the 17th century, it was standard to quote interest rates in hundredths. The term "percent" is derived from

200-438: A given THD is much more audible than clipping distortion at the same THD, since the harmonics produced by crossover distortion are nearly as strong at higher-frequency harmonics, such as 10× to 20× the fundamental, as they are at lower-frequency harmonics like 3× or 5× the fundamental. Those harmonics appearing far away in frequency from a fundamental (desired signal) are not as easily masked by that fundamental. In contrast, at

250-685: A loudspeaker, amplifier or microphone or other equipment produce a more accurate reproduction of an audio recording. In radio communications, devices with lower THD tend to produce less unintentional interference with other electronic devices. Since harmonic distortion can potentially widen the frequency spectrum of the output emissions from a device by adding signals at multiples of the input frequency, devices with high THD are less suitable in applications such as spectrum sharing and spectrum sensing . In power systems, lower THD implies lower peak currents, less heating, lower electromagnetic emissions, and less core loss in motors. IEEE Standard 519-2022 covers

300-492: A numeral, as in "5 percent" and not "five percent", the only exception being at the beginning of a sentence: "Ten percent of all writers love style guides." Decimals are also to be used instead of fractions, as in "3.5 percent of the gain" and not " 3 + 1 ⁄ 2 percent of the gain". However the titles of bonds issued by governments and other issuers use the fractional form, e.g. " 3 + 1 ⁄ 2 % Unsecured Loan Stock 2032 Series 2". (When interest rates are very low,

350-412: A party obtains 41% of the vote and this is said to be a 2.5% increase, does that mean the earlier result was 40% (since 41 = 40 × (1 + ⁠ 2.5 / 100 ⁠ ) ) or 38.5% (since 41 = 38.5 + 2.5 )? In financial markets, it is common to refer to an increase of one percentage point (e.g. from 3% per annum to 4% per annum) as an increase of "100 basis points". In most forms of English , percent

400-557: A percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is: It is not correct to divide by 100 and use the percent sign at the same time; it would literally imply division by 10,000. For example, 25% = ⁠ 25 / 100 ⁠ = 0.25 , not ⁠ 25% / 100 ⁠ , which actually is ⁠ 25 ⁄ 100 / 100 ⁠ = 0.0025 . A term such as ⁠ 100 / 100 ⁠ % would also be incorrect, since it would be read as 1 percent, even if

450-410: A price of $ 2.50 is an increase by a fraction of ⁠ 0.15 / 2.50 ⁠ = 0.06. Expressed as a percentage, this is a 6% increase. While many percentage values are between 0 and 100, there is no mathematical restriction and percentages may take on other values. For example, it is common to refer to 111% or −35%, especially for percent changes and comparisons. In Ancient Rome , long before

500-425: A surgical procedure That Handsome Devil , an American alternative rock band The IATA airport code for Thọ Xuân Airport The ICAO airline code for Thai Smile Transmitting Heading Device Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title THD . If an internal link led you here, you may wish to change the link to point directly to

550-488: A very similar THD R of 9.95%. However, at higher distortion levels the discrepancy becomes large. For instance, a signal with THD F 266% has a THD R of 94%. A pure square wave with infinite harmonics has THD F of 48.3% and THD R of 43.5%. Some use the term "distortion factor" as a synonym for THD R , while others use it as a synonym for THD F . The International Electrotechnical Commission (IEC) also defines another term total harmonic factor for

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600-533: Is a greater percentage of the sound produced at low volumes). THD is a summation of a number of harmonics equally weighted, even though research performed decades ago identifies that lower-order harmonics are harder to hear at the same level, compared with higher-order ones. In addition, even-order harmonics are said to be generally harder to hear than odd-order. A number of formulas that attempt to correlate THD with actual audibility have been published, but none have gained mainstream use. For many standard signals,

650-513: Is carried out and taught in different ways depending on the prerequisites and requirements. In this way, the usual formulas can be obtained with proportions, which saves them from having to remember them. In so-called mental arithmetic, the intermediary question is usually asked what 100% or 1% is (corresponds to). Example: 42 kg is 7%. How much is (corresponds to) 100%? Given are W (percentage) and p  % (percentage). We are looking for G (basic value). Due to inconsistent usage, it

700-483: Is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $ 200 and the price rises 10% (an increase of $ 20), the new price will be $ 220. Note that this final price is 110% of the initial price (100% + 10% = 110%). Some other examples of percent changes : In general,

750-414: Is often denoted using the percent sign (%), although the abbreviations pct. , pct , and sometimes pc are also used. A percentage is a dimensionless number (pure number), primarily used for expressing proportions, but percent is nonetheless a unit of measurement in its orthography and usage. For example, 45% (read as "forty-five percent") is equal to the fraction ⁠ 45 / 100 ⁠ ,

800-500: Is required that the manufacturer disclose the test signal frequency range, level and gain conditions, and number of measurements taken. It is possible to measure the full 20 Hz–20 kHz range using a sweep (though distortion for a fundamental above 10 kHz is inaudible). Measurements for calculating the THD are made at the output of a device under specified conditions. The THD is usually expressed in percent or in dB relative to

850-428: Is the same for a decrease of x percent, followed by an increase of x percent; the final amount is p (1 - 0.01 x )(1 + 0.01 x ) = p (1 − (0.01 x ) ) . This can be expanded for a case where one does not have the same percent change. If the initial amount p leads to a percent change x , and the second percent change is y , then the final amount is p (1 + 0.01 x )(1 + 0.01 y ) . To change

900-517: Is to say that the interest rate increased by 5%, which could theoretically mean that it increased from 10% per annum to 10.5% per annum. It is clearer to say that the interest rate increased by 5 percentage points (pp). The same confusion between the different concepts of percent(age) and percentage points can potentially cause a major misunderstanding when journalists report about election results, for example, expressing both new results and differences with earlier results as percentages. For example, if

950-530: Is usually written as two words ( per cent ), although percentage and percentile are written as one word. In American English , percent is the most common variant (but per mille is written as two words). In the early 20th century, there was a dotted abbreviation form " per cent. ", as opposed to " per cent ". The form " per cent. " is still in use in the highly formal language found in certain documents like commercial loan agreements (particularly those subject to, or inspired by, common law), as well as in

1000-629: The Hansard transcripts of British Parliamentary proceedings. The term has been attributed to Latin per centum . The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento . In some other languages, the form procent or prosent is used instead. Some languages use both a word derived from percent and an expression in that language meaning the same thing, e.g. Romanian procent and la sută (thus, 10% can be read or sometimes written ten for [each] hundred , similarly with

1050-595: The International System of Units and the ISO 31-0 standard require a space. The word "percentage" is often a misnomer in the context of sports statistics, when the referenced number is expressed as a decimal proportion, not a percentage: "The Phoenix Suns ' Shaquille O'Neal led the NBA with a .609 field goal percentage (FG%) during the 2008–09 season." (O'Neal made 60.9% of his shots, not 0.609%.) Likewise,

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1100-487: The ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total. (Similarly, one can also express a number as a fraction of 1,000, using the term " per mille " or the symbol " ‰ ".) If 50% of the total number of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male. An increase of $ 0.15 on

1150-434: The ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that ⁠ 60 / 100 ⁠ × ⁠ 5 / 100 ⁠ = ⁠ 3 / 100 ⁠ or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at

1200-411: The winning percentage of a team, the fraction of matches that the club has won, is also usually expressed as a decimal proportion; a team that has a .500 winning percentage has won 50% of their matches. The practice is probably related to the similar way that batting averages are quoted. As "percent" it is used to describe the grade or slope, the steepness of a road or railway , formula for which

1250-466: The "ratio of the RMS value of the harmonic content of an alternating quantity to the RMS value of the quantity" using a different equation. THD+N means total harmonic distortion plus noise. This measurement is much more common and more comparable between devices. It is usually measured by inputting a sine wave , notch-filtering the output, and comparing the ratio between the output signal with and without

1300-524: The English one out of ten ). Other abbreviations are rarer, but sometimes seen. Grammar and style guides often differ as to how percentages are to be written. For instance, it is commonly suggested that the word percent (or per cent) be spelled out in all texts, as in "1 percent" and not "1%". Other guides prefer the word to be written out in humanistic texts, but the symbol to be used in scientific texts. Most guides agree that they always be written with

1350-527: The Latin per centum , meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento , meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived. The percent value is computed by multiplying

1400-467: The RMS amplitude of the first harmonic, or fundamental frequency where V n is the RMS value of the n th harmonic voltage, and V 1 is the RMS value of the fundamental component. In practice, the THD F is commonly used in audio distortion specifications (percentage THD); however, THD is a non-standardized specification, and the results between manufacturers are not easily comparable. Since individual harmonic amplitudes are measured, it

1450-428: The THD F for complicated waveforms and filters often represents a difficult task, and the resulting expressions may be quite laborious to obtain. For example, the closed-form expression for the THD F of the sawtooth wave filtered by the first-order Butterworth low-pass filter is simply while that for the same signal filtered by the second-order Butterworth filter is given by a rather cumbersome formula Yet,

1500-439: The above criterion may be calculated analytically in a closed form. For example, a pure square wave has THD F equal to The sawtooth signal possesses The pure symmetrical triangle wave has For the rectangular pulse train with the duty cycle μ (called sometimes the cyclic ratio ), the THD F has the form and logically, reaches the minimum (≈0.483) when the signal becomes symmetrical μ  = 0.5, i.e.

1550-405: The above example, after an increase of x = 10 percent and decrease of y = −5 percent , the final amount, $ 209, is 4.5% more than the initial amount of $ 200. As shown above, percent changes can be applied in any order and have the same effect. In the case of interest rates , a very common but ambiguous way to say that an interest rate rose from 10% per annum to 15% per annum, for example,

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1600-399: The answer: ⁠ 3% / 10% ⁠ = ⁠ 30 / 100 ⁠ or 30% of all computer science majors are female. This example is closely related to the concept of conditional probability . Because of the commutative property of multiplication, reversing expressions does not change the result; for example, 50% of 20 is 10, and 20% of 50 is 10. The calculation of percentages

1650-410: The closed-form expression for the THD F of the pulse train filtered by the p th-order Butterworth low-pass filter is even more complicated and has the following form: where μ is the duty cycle , 0 < μ < 1, and Percent In mathematics , a percentage (from Latin per centum  'by a hundred') is a number or ratio expressed as a fraction of 100. It

1700-471: The existence of the decimal system, computations were often made in fractions in the multiples of ⁠ 1 / 100 ⁠ . For example, Augustus levied a tax of ⁠ 1 / 100 ⁠ on goods sold at auction known as centesima rerum venalium . Computation with these fractions was equivalent to computing percentages. As denominations of money grew in the Middle Ages , computations with

1750-399: The fundamental as distortion attenuation. A variant definition uses the fundamental plus harmonics as the reference: These can be distinguished as THD F (for "fundamental"), and THD R (for "root mean square"). THD R cannot exceed 100%. At low distortion levels, the difference between the two calculation methods is negligible. For instance, a signal with THD F of 10% has

1800-404: The fundamental, and so on, in addition to harmonic distortion. For psychoacoustic measurements, a weighting curve is applied such as A-weighting or ITU-R BS.468 , which is intended to accentuate what is most audible to the human ear, contributing to a more accurate measurement. A-weighting is a rough way to estimate the frequency sensitivity of every persons' ears, as it does not take into account

1850-404: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=THD&oldid=1051383710 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Total harmonic distortion In audio systems, lower distortion means that the components in

1900-462: The intent was to say 100%. Whenever communicating about a percentage, it is important to specify what it is relative to (i.e., what is the total that corresponds to 100%). The following problem illustrates this point. In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female? We are asked to compute

1950-478: The non-linear behavior of the ear. The loudness model proposed by Zwicker includes these complexities. The model is described in the German standard DIN45631 For a given input frequency and amplitude, THD+N is reciprocal to SINAD , provided that both measurements are made over the same bandwidth. The distortion of a waveform relative to a pure sinewave can be measured either by using a THD analyzer to analyse

2000-433: The number 0 is included if the interest rate is less than 1%, e.g. " 0 + 3 ⁄ 4 % Treasury Stock", not " 3 ⁄ 4 % Treasury Stock".) It is also widely accepted to use the percent symbol (%) in tabular and graphic material. In line with common English practice, style guides—such as The Chicago Manual of Style —generally state that the number and percent sign are written without any space in between. However,

2050-426: The numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1,250 apples, one first computes the ratio ⁠ 50 / 1250 ⁠ = 0.04, and then multiplies by 100 to obtain 4%. The percent value can also be found by multiplying first instead of later, so in this example, the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1,250 to give 4%. To calculate

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2100-442: The onset of clipping, harmonics first appear at low-order frequencies and gradually start to occupy higher-frequency harmonics. A single THD number is therefore inadequate to specify audibility and must be interpreted with care. Taking THD measurements at different output levels would expose whether the distortion is clipping (which decreases with an decreasing level) or crossover (which stays constant with varying output level, and thus

2150-449: The original frequency. THD is a measure of that additional signal content not present in the input signal. When the main performance criterion is the "purity" of the original sine wave (in other words, the contribution of the original frequency with respect to its harmonics), the measurement is most commonly defined as the ratio of the RMS amplitude of a set of higher harmonic frequencies to

2200-469: The output wave into its constituent harmonics and noting the amplitude of each relative to the fundamental; or by cancelling out the fundamental with a notch filter and measuring the remaining signal, which will be total aggregate harmonic distortion plus noise. Given a sinewave generator of very low inherent distortion, it can be used as input to amplification equipment, whose distortion at different frequencies and signal levels can be measured by examining

2250-491: The output waveform. There is electronic equipment both to generate sinewaves and to measure distortion; but a general-purpose digital computer equipped with a sound card can carry out harmonic analysis with suitable software. Different software can be used to generate sinewaves, but the inherent distortion may be too high for measurement of very low-distortion amplifiers. For many purposes, different types of harmonics are not equivalent. For instance, crossover distortion at

2300-411: The price (a decrease of $ 22), then the final price will be $ 198— not the original price of $ 200. The reason for this apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different initial values ($ 200 and $ 220, respectively), and thus do not "cancel out". In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount

2350-472: The pure square wave . Appropriate filtering of these signals may drastically reduce the resulting THD. For instance, the pure square wave filtered by the Butterworth low-pass filter of the second order (with the cutoff frequency set equal to the fundamental frequency) has THD F of 5.3%, while the same signal filtered by the fourth-order filter has THD F of 0.6%. However, analytic computation of

2400-414: The recommended practice and requirements for harmonic control in electric power systems. To understand a system with an input and an output, such as an audio amplifier, we start with an ideal system where the transfer function is linear and time-invariant . When a sinusoidal signal of frequency ω passes through a non-ideal, non-linear device, additional content is added at multiples nω (harmonics) of

2450-469: The sine wave: Like the THD measurement, this is a ratio of RMS amplitudes and can be measured as THD F (bandpassed or calculated fundamental as the denominator) or, more commonly, as THD R (total distorted signal as the denominator). A meaningful measurement must include the bandwidth of measurement. This measurement includes effects from ground-loop power-line hum, high-frequency interference, intermodulation distortion between these tones and

2500-438: Was p , the final amount is p (1 + 0.01 x )(1 − 0.01 x ) = p (1 − (0.01 x ) ) ; hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number). Thus, in the above example, after an increase and decrease of x = 10 percent , the final amount, $ 198, was 10% of 10%, or 1%, less than the initial amount of $ 200. The net change

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