Best Speaker Cables of 2022: Budget vs. Premium Audio Cables

To fully enjoy the capabilities of your audio system, you need to choose the right cable for it. Low-quality models can significantly spoil the sound - distort the signal, deform the sound, produce extraneous noise and reduce power. Of course, a good model will not improve the performance of the system, but it will allow it to realize its full potential. There are a large number of models on the market. How to choose the most suitable one for you? Our review will tell you what guidelines will help you avoid making mistakes when choosing. The editors of the Yanashla website present a rating of the best speaker cables for 2022.

Technical characteristics and design

Typically, for the cables in question, the conductive cores are made of copper. This material is optimally suited for the purpose of transmitting electrical signals, because it is wear-resistant, and it is able to accurately transmit different sound frequencies. Cables typically use commercial copper (this option is very economical), but oxygen-free copper, which has improved conductivity, can also be used. The best option is still considered to be pure copper, which is capable of creating excellent sound transmission.

Another metal option for making cores can be silver. The use of silver is on an extremely small scale due to its high cost. However, it is silver that has excellent electrical conductivity, which fully guarantees the quality of broadcasting.

IMPORTANT! The quality of the wire will not only be determined by the core material - the insulation of the wire will also play an important role in this matter. The period of operation, as well as the predisposition to the transmission of extraneous noise and interference, will depend on its positive properties.

To insulate the acoustic cord, either polypropylene or Teflon is used. The latter material is preferred, but is rarely used. Polyvinyl chloride is more common as an insulation material, but it is often inferior in its characteristics to the two above-mentioned types of material, and in some cases it can even distort the sound.

Structurally, the object under consideration consists of one or more conductive wires, which, in principle, does not affect signal transmission, but its strength will depend on the number of wires. Thus, the more people lived in it and the thinner they are, the greater the elasticity of the object and the lower the risk of its fracture.

Also, one of the most important characteristics of the audio cords under consideration is their cross-sectional diameter. Traditionally, this parameter varies from 0.25 to 4 square millimeters. It is necessary to select the cross-sectional diameter based on the intended tasks for the wire. Thus, the instructions for audio systems, as a rule, contain information about the recommended caliber of the speaker cord . If such information is not available, then the required cross-sectional diameter needs to be calculated based on the following data: the resistance of the material and the power of the amplifier or speaker, coupled with the length of the wire. If the diameter is not wide enough, then its ability to transmit the entire frequency range will decrease, which will clearly affect the sound. However, the more wire there is and the larger its diameter, the higher its cost.

Audio cables

The first cable is shown in Figure 1. This is a very cheap but decent cable with a cross section of 2.5 mm2 and costs about 2...3 dollars per meter. It is recommended to use a cable of this cross-section if the distance from the amplifier to the speakers is 3...5 meters. Especially for low impedance speakers. This cable is similar to the "regular" cable examined last time.

The name of the cable on the graphs is “2.5 mm2”.

Rice. 1.

The second cable is a little nicer. Its conductors are made of twisted bundles of ordinary and tinned copper, which is quite beautiful, Fig. 2. And the cable insulation is also more “noble” - square section. And the inscriptions on the cable: OFC and Hi-Fi. It is clear that you can write anything you want, but the buyer is pleased. Technically, this cable design has no advantages. It is recommended to use a cable of this cross-section if the distance from the amplifier to the speakers is no more than 3 meters.

The cost of such a cable is about 1.5...2 dollars per meter, so this is also an ordinary cheap speaker cable.

The name of the cable on the graphs is “1.5 mm2”.

Rice. 2.

The third cable (Fig. 3) is even more beautiful, especially since it is a monster! At least that's what it says on the cable itself - MONSTER. This cable has taken measures to reduce skin effect. The center of the cable is a thin (about 1 mm) polyethylene rod, and on top of it are ordinary copper conductors, Fig. 4. Thus, from the central region of the cable, “where no current flows,” the copper is removed and transferred to the outer layer, where the maximum current flows.

The name of the cable on the graphs is “Low skin”.

Rice. 3.

Rice. 4.

This cable was included in previous cable testing, and indeed, it has slightly less skin effect than conventional cables.

The fourth cable with reduced inductance. The principle of its design is shown in Figure 5. These are four cables with a cross-section of 0.75 mm2 folded together in such a way that the forward conductors (red in Figure 5) of one cable are located above the return conductors of the other cable (blue in Figure 5). With this relative arrangement of the wires, the magnetic fields they create are subtracted and compensated. As a result, the total magnetic field of this entire complex cable decreases, which means its inductance also decreases.

Rice. 5.

Since such a cable is assembled from conductors of small cross-section, the skin effect in it is reduced along with the inductance. The appearance of the cable is shown in Figure 6. This cable also took part in the previous study.

The name of the cable on the graphs is “Low L”.

Rice. 6.

Types of speaker cables

As a general rule, they can be divided into single (monolithic) and multi-core. Further division occurs into three main types:

• Bundle-shaped ones are the worst option for transmitting sound, because the cores in such a wire are placed unevenly, and this has a significant impact on the sound quality. Moreover, the bundle-shaped structure of the cord weakly suppresses extraneous noise.
• Concentric - in such a wire, the cores inside are evenly spaced. Such options have a constant cross-section along the entire length, which indicates high quality sound transmission.
• Rope wires - these wires are, in fact, an improved model of concentric ones. Their structure implies a geometrically correct interlacing of veins inside, which indicates enhanced elasticity indicators.

Channel Penetration Compensation

Is it possible to fix the situation without replacing the wire? Yes, definitely. And this may be relevant for cases:

• The presence of resistance at the source, where, for example, thin tracks go to the headphone jack (in smartphones, Hi-Fi players).
• The headphones have a non-removable cable, the headphones are not removable and there is no desire to lose the warranty.

You can reduce the effect by adding resistors in series to the wires. In the on-line calculator this will be expressed as an increase in RAmp Out.

Photo from the HiFiShow 2022 exhibition, where what this material was about was demonstrated.
The adapter with red resistors just showed what change an increase in the output resistance of the amplifier makes. And the second adapter showed changes in sound with increasing resistance along the common wire. If in a combination of headphones and a source the penetration of channels is in phase, then you need to add a resistor to the common wire, creating additional mixing in antiphase.

If in a combination of headphones and a source the penetration of channels is in antiphase, then you need to add a resistor between the signal wires, adding in-phase mixing.

A very important point! If the source has analog volume control, then usually the output impedance of the amplifier changes slightly at different volume levels. And this small change is enough for the compensation to stop working.

Thus, it is possible to make compensation in hardware through an additional adapter, but this is a rather complicated method that will require installing not only a constant resistor, but also a trimmer with constant calibration. A method for those audiophiles who are “obliged to suffer” by default.

But programmatically, through foobar2000 with special plugins, you can compensate for the penetration of channels, and vice versa, listen to how the sound changes with a “bad cable”. More on this below.

Factors affecting sound transmission

The Impact of Impedance on Audio Broadcasting

This factor begins to influence the dynamics of sound transmission as a whole, in the case when it (resistance) exceeds 5% of the total impedance of the speakers. The formation of resistance is influenced by two parameters:

• Speaker cable length;
• Cross-sectional area.

It is worth noting that the shorter the speaker cord, the less resistance is generated. Professionals advise to ensure the best sound conditions by keeping the speaker cable as short as possible (wherever possible), but also ensuring that the amplifiers (speakers) are as far apart as possible. This suggests that the resistance will be proportional to the length of the wire, and therefore, with a shorter cable length, the resistance will be minimized. And it is necessary to space speakers and amplifiers further away from each other in order to maintain proper stereo effect.

IMPORTANT! Still, it’s worth trying to ensure that the length of the wires to each speaker more or less coincide with each other, even if they are shortened as much as possible. In this simple way it is possible to balance the entire system much better.

Regarding the effect on the cross-sectional resistance, the following rule will work here: the lower the sensor is located and the thicker the wire, the less resistance will be created. The main thing is not to exceed the total resistance threshold produced by the amplifier (or speakers).

Single-cable and dual-cable connection

Broadcasting sound to speakers or an amplifier can occur through connection with one or two cables. Naturally, even a speaker that has two outputs for speaker cables can be connected with one cable, but a double connection is considered preferable. The whole point is that dual connection allows you to create a more open sound space, and its detail is significantly increased. On the other hand, connecting with a single cable can create a more monolithic and organic musical sound. This quality of single-cable connection may be required in special circumstances (for example, when broadcasting music in tight spaces).

IMPORTANT! It is worth noting that a two-cable connection will always cost more than a single-cable option.

The importance of speaker cable direction for transmission quality

Acoustics professionals ensure that directional sound always delivers the best sound. This suggests that in order to obtain a better direction of sound, the cable transmitting it must be laid in a certain direction. Therefore, the connection must be made in such a way that the direction imprint indicated on the wire insulation is read in the same direction as the signal being transmitted. The specified connection diagram will best affect the synchronization of sound and the overall consistency of the entire assembled audio system. Practice shows that if the wire is not connected in the direction of the signal, then its clarity can decrease within the range from “insignificant” to “below average”.

"Warming up" the speaker cable

Professionals say that the new cable needs to be “warmed up” in order to achieve its peak in the quality of the transmitted sound. Such “warm-up” involves operation (with interruptions, of course) after the initial connection for at least 150 hours. As it “warms up,” the quality of the signals it transmits will also change, which, when comparing the first activation and the last, can be noticed simply by comparing microphone recordings of the output audio.

What is channel interpenetration

Spectra of the signal of the left channel and the mixed right one

The channel crosstalk parameter shows the level of channel mixing when audio from the left channel is additionally played in the right channel and vice versa.

The less channel penetration, the better, because it's closer to the sound of the original recording.

The parameter is expressed in decibels. The graph above shows how when the left channel (blue spectrum) is played, the signal bleeds into the right channel (black spectrum). The amplitude difference in the example is 50 dB (-31 and -81 dB at 693 Hz). Because parameter shows the difference, then the value can be either positive or negative and mean exactly the same thing. The larger the number, regardless of sign, the better.

The final graph displays the curve over the entire frequency range. Technical specifications usually give a value for a frequency of 1 kHz.

The main names for this parameter are:

• Interpenetration of channels
• Crosstalk
• Crosstalk

Some people do this test using RMAA and a sound card. Such results are most often incorrect. When testing, the test signal must be produced by one device and recorded by another device, and these devices must have a separate ground. When testing through a sound card, against itself, the ground is common and the result will be close to ideal. Those. It is not the RMAA that will “lie” here, but a technically incorrectly organized test.

How speaker cables work with speakers

A proper speaker cable is one that has low resistivity and excellent electrical conductivity. Samples based on pure copper are perfect, because the amount of impurities in it does not exceed 1%. Also, for speakers it is advisable to use wires whose windings are made of noble metals (naturally, this option will not be cheap). In cases where speakers are used over a large area of ​​the room, a silver core in the wire will be an ideal solution (moreover, it will significantly reduce the resistance compared to copper). But you shouldn’t use a product with a tin coating for working in spacious rooms - it will poorly transmit high-frequency sounds.

Selecting a wire for a speaker is quite easy, making the necessary calculations step by step:

• First you need to find out the maximum possible resistance for the cable. To do this, the resistance value of the connected speaker (indicated on its body) is multiplied by 0.05.
• Then you need to calculate the existing resistance, which looks like the length of the cable, multiplied by the value of the resistance of the material of its manufacture, and divided by the cross-sectional area.
• At the end, you should compare the results of the first and second actions. If the second result exceeds the first by more than 5%, then such a cable cannot be used.

If you have problems with exceeding the result, you can try to shorten the length of the cord or you will have to use a cord with a larger cross-section.

IMPORTANT! Any audio cord connected to speakers must be flexible and elastic, its insulation must not be damaged, and it must be even and round along its entire length.

Connecting to speakers

First of all, you need to make sure that all elements of the audio system are disconnected from the power supply. When connecting the cord to the speakers, observe polarity by using the color markings (or plus/minus symbols) on the speakers and cord. When connecting wires to audio speakers, you need to take into account the features of their connectors:

• Only bare wires are inserted into the spring terminals. The mechanism of such connectors securely fixes the cable and is easy to remove/insert. However, banana or spade type products cannot be connected to such a connector.
• All types of plugs can be used for connection via screw terminals. To connect the “spade” or bare wires, you just need to unscrew the nut and clamp the connector with it. “Double and single bananas” can be inserted directly into the terminal hole and there is no need to unscrew the nut.

IMPORTANT! It is worth noting that connecting bare wires to spring clamps is the most effective, since it is believed that such a clamp will provide more reliable contact.

Audio cable measurements

An example of a measurement result is shown in Figure 7. In principle, you can use such results, they are quite good. But for greater convenience, I exported the measurement results to Excel and built more convenient and visual graphs there.

Rice. 7.

Measurements were carried out in the range from 100 Hz to 100 kHz. It makes no sense to use lower and higher frequencies. The step along the frequency axis was equal to 1/6 octave, which provided excellent frequency resolution. Figure 8 shows an example of a graph generated from the measurement results. The graph shows the points at which measurements were made - there are sixty of them. In other graphs, such points are not shown for greater clarity of the graphs.

Rice. 8.

Difficulty of choice

When purchasing an acoustic cable, you first need to pay attention to the inner core by feeling it. If the wire seems too stiff, then this is a reason for doubt. It is possible that the core is not made of copper, but of a copper-plated alloy, the conductivity of which leaves much to be desired.

IMPORTANT! The seller may insist that a copper-plated alloy is used in the speaker cable to prevent possible corrosion. However, such a statement is an obvious marketing ploy, because with proper insulation, the acoustic wire will have to be in conditions of high humidity for a VERY long time before corrosion processes begin.

As a result, you need to focus on the following points when purchasing:

• High-quality cord insulation should not stick to your hands and leave staining marks. To the touch, the insulation should be moderately elastic and soft, however, it must maintain sufficient strength and not break if excessively bent. Double insulation will increase the service life of the wire, but will also cost more.
• The color marking should be an easily distinguishable color and shade, otherwise it is possible to get confused when connecting, because the colors will not match the incoming terminals. This is especially important for surround sound systems, because If connected incorrectly, you can “burn” the speakers (and in the worst case scenario, the entire audio system).
• If a product is purchased “to be cut,” then a reputable manufacturer always supplies its products with meter marks so that the cable can later be shortened by cutting it to the required length.
• Naturally, if you find products from a well-known brand at a “thrift” price, you should look for its products in open sources and compare both the appearance and technical characteristics with those of the found cheap sample.

Statistics

Based on statistical data from measurements of more than 500 headphones by the Reference Audio Analyzer project, we can draw some conclusions.
Most in-ear headphones have a cable resistance of 2 to 3 ohms. In this case, the cable resistance also includes the plug resistance of 0.5-1 Ohm. You can change the cable, but without fanaticism and based on the collected subjective experience of audiophiles, without the chance that any measurement will show a clear increase in quality.

For most full-size headphones, the cable resistance varies widely, from 1 to 10 ohms. Here, if you have an amplifier with a low output impedance, it sometimes makes sense to reduce the cable resistance, because for low-impedance headphones, the cable resistance additionally affects the volume - there is a chance to make the operating conditions of the amplifier easier.

Operating rules

Before connecting the speaker cable for the first time, you must carefully inspect it for integrity, carefully checking the connectors, connectors, terminals and insulation. As a rule, the manufacturer, during the operation of its products, advises customers to follow the simplest rules:

• Do not bend, squeeze or twist the cord too much;
• The cord should not be placed parallel to the network wires (this prohibition applies to absolutely all devices and structures containing ferrite components);
• The ends of the wire must be completely hidden in the connectors;
• It is strictly forbidden to combine “positive” and “negative” conductors to avoid a short circuit;
• If the cord is not in use, it should be removed from the connector;
• The wire contacts must periodically undergo a cleaning procedure in order to avoid the appearance of traces of oxidation on them;
• To maintain high-quality sound, do not use wires that are too long.

Methods for self-testing

Step-by-step instructions are provided on separate pages. There are currently two methods. The simplest and fastest way is possible through the foobar2000 software player with special plugins. The second method contains special test tracks that can be played on any device.

foobar2000

Because This is a version of foobar2000 for Windows, then this method is not yet available to users of other OSes (but if you work reasonably well with sequencers, then once you understand the principle, you can do this on any OS. Before plugins for foobar2000 were made, experiments were carried out with the Ableton sequencer Live). Go to instructions and plugins

Test tracks

The second method does not depend on the OS and can be used with any playback source, including Hi-Fi players such as low-end FiiO, iBasso or low-end budget Hi-End Walnut. Go to instructions and test tracks

If foobar2000 is not on the list of your favorite players, contact the authors of other players with a request to make similar plugins. The mathematics of these plugins is extremely simple and does not require any patents, licenses, or particularly deep knowledge in psychoacoustics. Important! In addition to calculating the channel penetration level using the crosstalk plugin, you can both compensate for channel penetration and listen to:

• What will improving the wire do?
• What does this channel penetration actually sound like? How does it compare to the numerical values ​​in dB?

Instead of an epilogue

An analysis of the market for the materials in question has established that its composition is by no means homogeneous, and there is no gradation on it, as such. In principle, all speaker cables can be divided into “budget” and “extra-expensive”. There is simply no middle management. This situation is due to the fact that with the use of expensive materials (noble metals) in construction, the price of these goods simply jumps several hundred times. However, with the help of such noble components, it is possible to achieve maximum sound quality. It is somewhat regrettable that the domestic manufacturer is practically not represented on this market (at least, such products are simply not available among popular materials).

Start

I have already written an article about the skin effect: Skin effect in an audio cable. What is it, where does it come from and why we don't need to be afraid of the skin effect in audio cables. I also measured the actual skin effect on some audio cables. The measurement results are presented in the article Real skin effect in cables. They confirmed the theory: the skin effect practically does not appear in audio cables, and there is no point in being afraid of it. Fighting the skin effect also makes no sense.

The main enemy of an audio cable is its inductance. It is the increase in inductive reactance with frequency that can lead to increased signal attenuation in an audio cable at high frequencies. Therefore, it makes sense to manufacture cables not with a reduced skin effect, but with a reduced inductance. Although in fact, manufacturers do not do what is beneficial to us, the buyers, but what is beneficial to them, the producers. And then, with the help of marketing and advertising, they convince us to buy these particular products.

In the articles linked above, actual measurements were performed only at a few frequencies, which reduced the clarity of the results. Recently I came across measuring equipment that made it possible to measure the properties of an audio cable at various frequencies. So I selected four of the most representative audio cables and measured their properties. Two of these cables were also used in previous measurements, so the experimental results can be compared. Another cable is very similar to the one used last time. So these measurements of mine can be considered an addition to the previous ones.

All cables are copper and designed for audio.

No esotericism

By the way, it’s also worth saying that QED writes a lot about how their engineers understand the influence of cables and why they choose certain designs. And in all this, I personally don’t see any crazy esotericism, it’s a completely decent technical approach. However, esotericism also sometimes plays, but that’s another story, not about QED.

Methodologically, I built the test quite simply - one well-known system with a decent (and also familiar) cabling and several alternating QED listening sessions “under the protocol”. And in case the need arises to compare something else with something else, I always have a certain supply of a wide variety of cables.

QED Supremus Airloc Connectors

As a generalization, I will say that the break-in process of both the XT25 and the Supremus is no different. The sound floated back and forth a little, opened up a little. But it wasn’t that it was impossible to listen to the first 200 hours. From what was there at the beginning, but disappeared in the process, I will note the sharpness and slight synthetic quality.

Elevation QED XT25

First, I’ll tell you how the younger model performed. The sound is slightly light, with a slightly elevated mid-high range. However, without emphasized sharpness. The presentation is clean, textured, and neat. There seems to be elation and joy, but at the same time there is also neatness. The bass is of moderate depth, slightly forced, but not bloated. In general, in the lower range there is a certain feeling of basis, as if some kind of line has been drawn. The nuances of the bass are slightly superficial, perhaps a little formal, but without confusion and without a feeling of lag. The middle is relatively smooth, more transparent than one might expect. Higher up, as I already said, there is a certain elation felt, but not at all beyond the bounds of decency - the cable was unable to produce a sharp or annoying sound under any conditions.

QED Supremus Airloc. The photo shows both the internal structure and the place where the cable is pressed into the connector

The detail is not incredible, but the level is definitely better than expected. It is expressed something like this: up to a certain limit, everything is clearly audible, and then (based on subtle nuances, details and halftones) a rather sharp decline appears. The dynamics are very good, better than expected. You can only notice a certain loss of harmony and confusion in the sound on complex symphonic recordings, and even then not to such an extent that it would be supercritical.

In general, the sound seems to be trying to be correct, honest, neat, but not tight, but rather open. In it you can probably find a light character, but not flashy, but rather a calm, matte-rounded one.

The scene turned out to have good depth, but less wide than in the case of the control cable harness. There is air, but not very much of it, although the echeloning of scene images is normal, only the drawing of contours is not very distinct.

QED Supreme

Overall, the XT25 did very well. I took some cables that happened to be at hand for comparison - and in similar conditions they have worse results. The range is more skewed, there is some kind of inappropriate warmth, the mess in the sound manifests itself in simpler music. Therefore, for its “almost free” price tag, the XT25 performed very well. And this is taking into account the fact that it worked in a system of a much higher level than those in which the cable may be found in real conditions.

Musical material:

• Audio Accessory - T-TOC Records High Quality Data Master Comparison, TDVD-0002, DVD-R, ripy 16/44.1, 24/96, 24/192 FLAC.
• Stereo Sound Reference Record. Jazz&Vocal, Stereo Sound, SSRR4, SACD/CD.
• Stereo Sound Reference Record. Popular Selection, Stereo Sound, SSRR5, SACD/CD.
• Brian Eno, Craft On A Milk Sea, Warp Records, FLAC 24/44.1.
• Carmen McReae, Book of Ballads, Kapp Records/Universal Music Japan, UCCU-9634, SHM-CD.
• Depeche Mode, Personal Jesus, Sire/Reprise 21328-2, MS CD.
• George Michael, Faith, Epic/Sony Music, 7753020, Special Edition 2 x CD+DVD.
• John Lennon, Imagine, Capitol/Mobile Fidelity, UDCD 759, gold-CD.
• Laurie Anderson, Homeland, Nonesuch, 524055-2, CD+DVD.
• Pat Martino, East!, Prestige/Mobile Fidelity, UDSACD 2022, SACD/CD.
• Radiohead, The King of Limbs, Ticker Tape Ltd., TICK-001CDJ, Blu-spec CD.
• R-men, I thought about you, T-TOC Records, MCDR3002, CD-RIIα.
• Suzanne Vega, Close-Up. Vol 1, Love Songs, Amanuensis Productions/Cooking Vinyl, COOKCD521, CD.

Translated by Artyom Avatinyan

Transparency QED Supremus

Now let's see how QED Supremus worked. The first sensation is a high, emphasized transparency, a “washed” sound. Good resolution, lots of details. Sometimes it seems that absolutely everything in a sound is important, every note and every after-sound. However, there is no pretentiousness in such a presentation; it does not tire you with the flow of secondary information, since the priorities are set correctly and the balance is maintained. But the feeling that there is a lot of sound, it is rich and multifaceted does not disappear during the listening process, it just very quickly begins to be perceived as something close to natural.

The bass in this case is not extremely deep, there is some composure, which feels almost the same as that of a junior cable, but the quality of the bass itself, of course, is different - everything is more precise, more textured, more varied.

The packaging of QED Supremus is simple from the inside, no frills

Some lightening and slight elevation of the mid-upper range are also present (here it is appropriate to think about the general style and style of the QED sound), but excessive brightness or harshness is not noticeable. On the contrary, with the existing qualities one can note some restraint, lack of laxity or excessive emotional emphasis.

The dynamics and detail are smooth, confident, without distortions, without forceful forcing. Everything somehow fits together quite seamlessly into a single picture, and this picture, in turn, looks very good. The sound cannot exactly be called boring, but it is not emotionally oversaturated either. Apart from a slight (again, matte-neat) lightening of the sound, there is no coloration of any kind. Moreover, based on the example of comparisons during the test, I can definitely say that warm-soft is definitely not about this cable. Even if you listen to something heartbreaking and emotional, satiety is not noticeable. Although I absolutely cannot say that emotions or anything else are simplified to any extent, there is no such thing.

QED Supremus packaging

Thus, the presentation can be considered almost monitor-like, unobtrusive and quite honest. Although not perfectly neutral.

On complex fragments, you can occasionally hear a slight simplification of the sound, which may become a little more formal, but no mess or turbidity is formed even on such material as “Requiem” by Giuseppe Verdi. With the caveat that it does not occur only if the rest of the system is able to cope with such music, because, of course, the role of the cable is not paramount here. However, it did not prove to be a bottleneck.

The scene is quite correct in construction and proportions, without exaggerated scale or obvious intimacy, with good depth and width. The air feels moderately neat, images and plans are readable. Smooth, balanced result without distortions.