On Frequency Response Plots

Of late, two camps have emerged, and fights are starting to break out over the use of Frequency Response plots in personal audio.  One side insists if the graph doesn’t look like they think it should then the earphone in question should be thought of as garbage, the other side argues that graphs can’t hear and are thus a poor indicator of how something sounds.      This is a case of both sides making some good points, but both take it too far and it becomes a battle of reductio ad absurdum in order to prove the other side is wrong.

 

Fact is Frequency Response (FR) plots can give useful information about what is possible, but cannot define all aspects that should be considered. 

 

Before going into more detail on what we can expect to learn, let’s make sure we all have the same definition.  A Frequency Response graph or FR plot is created by feeding a sine sweep at a given voltage or current (maintained as a constant) to a speaker and then taking a series of measurements of the output using a calibrated microphone.   At set intervals along the sweep, measurements are taken and transformed to show both frequency and amplitude.   This quantifies the output signal.  Those values are then plotted for each input value to create the FR Plot.    The FR plot can actually be thought of as a series of individual measurements (independent of each other) that are then plotted on a graph and a best-fit line added.  

 

What an FR plot can tell us:

FR plots show what frequencies the driver/s  is/are capable of producing and at what tolerance.   A value of 20Hz-20,000Hz +/- 3db tells us that we should expect the speaker to produce sound with roughly the same amplitude for the entire audible spectrum.  Often, FR values for speakers and headphones are listed as 20-20,000Hz but without specifying a tolerance.  This is a way to dodge the fact that many would show a dramatically decreased frequency range if limited to +/- 3dB range   (ie 140Hz – 11,376Hz).   Generally speaking +/- 3dB is used for drivers and +/- 5dB is becoming more common as well.     This gives us an estimate of the range of frequencies we can expect to hear. 

If a plot shows that a driver has a large drop below 75Hz (roll-off), it tells us the driver will struggle to produce adequate volume for any tone below that point.  Likewise, if the plot drops to near zero (0) at 12kHz, then the driver is not going to reproduce tones above that point.

Attempting to use EQ to augment bass or treble will only work in the first scenario where the level is lowered, but not absent.  In that case, one can increase the strength of the input signal at that frequency to enhance the output quantity.  In the second case, nothing one can do is going to introduce a frequency that the driver is incapable of reproducing.  If the driver rolls-off notably, chances are the frequencies below that cannot be augmented sufficiently to bring them into line with the rest of the signature.

 

What an FR Plot can’t tell us

The first mistake often made in claiming an FR plot shows us the sound signature of a device.   Quite simply, it cannot as the way it hears, is not the same way we do.

 

The plot is created by taking a series of discrete measurements using a single frequency reference point and quantifying the output at that frequency.    For Example, Middle C (C4) is 261.63Hz, but the harmonics produced by when a piano plays a C4 are 261.63Hz (1st), 523.26Hz (2nd),784.89Hz (3rd), 1046.52Hz (4th), and so on.   Our ear hears those higher order harmonics, not just the primary tone.  Our measurements exclude all but the primary tone, thus accounting for one of the differences in what we hear, vs what we see on a plot.   Each instrument has different harmonics as they are dependent on the length of the string or tube (for wind and brass instruments).  The differences in harmonics between instruments are what allow us to tell the difference in a trumpet playing C4, and a Saxophone playing C4.  If reduced to just the primary frequency, the instruments sound exactly alike.  Since timbre is determined by which harmonics are present and in what proportion, this information is critical in determining the performance of a driver.

 

This also points to another related shortcoming of the FR plot.  It tells us nothing about how tones interact or overlay one another as each measurement is of a single distinct frequency and not a combination of frequencies.    This means an FR plot cannot be used to learn anything about layering.      On a piano, C4 produces a 2nd order harmonic at 523.26Hz and will contribute to what we hear as the Tenor C (C5) at that higher frequency.   If no instrument is playing a C5 note at the same time, that tone will be below the primary tone in amplitude, but if another instrument is playing C5, then the amplitude is raised by the addition of the harmonic.

The FR also cannot be used to determine a driver’s imaging capabilities or soundstage either.  It simply lacks any useful information from which to draw these conclusions.  Imaging and soundstage are created in our brain by analyzing the timing of the sound.  A sound that arrives at one ear sooner than the other is interpreted by the brain as being closer to the side where the sound arrived first.    A sound only played on one side or the other (in earphones) will be heard as coming from left front or right front respectively.   A sound played on both with a fraction of a second delay in one or the other will appear to move as the amount of delay changes.   Echos are even more complex as they not only deal with delay, but also with changes in frequency due to partial absorption and partial reflection of sound by the barrier creating the echo.   Since FR tells us nothing about the attack or decay speed of a driver, it tells us nothing of the limits of resolution needed to produce realistic spatial cues or echos.  

 

Conclusions:

  • An FR plot can be a useful tool if created properly and used properly
  • They are often created improperly.
  • They are often misinterpreted.
  • What is on an FR chart will never 100% match what you hear due to the differences in the measurement methods and human hearing
  • FR cannot tell us about the interaction of multiple tones, soundstage, or imaging characteristics all of which are important to reproduction of music.

As you can see, I am not a member of either camp,  I don’t believe that FR plots are without some merit, nor do I think they can be used as the sole judge of a product.  Like any tool, they provide useful service only when wielded properly.      I will continue to include FR charts in my reviews, as I think they are a good tool for comparative analysis and as such I have setup my system slightly differently than some.

I used a fixed input level (voltage) rather than trying to produce an 85dB tone at 1kHz like many others.  I do this because the amplitude of the plot then gives a way to compare how easy or hard to drive a an earphone is to others I have reviewed.  If the same input produces 87dB on one and 82dB on another product (both at the same reference point of course) we can assume the higher amplitude is the easier one to drive.      Plots usually fall within a few dB one way or the other so it is rare that two items differ enough to need an enlarged axis to cover both (he6 for example).

As always, I welcome comments and thoughts, but flames will be promptly deleted.

 

1 thought on “On Frequency Response Plots

  • August 16, 2019 at 13:00
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    I agree with the conclusion but dispute the facts claimed in the process of deriving said conclusion…
    FR plots are hard to derive sound signature from but not because of the reasons you stated.

    “The plot is created by taking a series of discrete measurements using a single frequency reference point and quantifying the output at that frequency.” Actually FR is often measured using continuous (as opposed to discrete) sweep measurements, which sweep through every possible frequency in the audible spectrum.
    “Our ear hears those higher order harmonics, not just the primary tone. Our measurements exclude all but the primary tone,” True, but the harmonics of all HiFi headphones are at a vanishingly low level. It’s called “harmonic distortion”–nobody wants distortion in their HiFi equipment and it has been nearly eliminated. When it is present in noticeable amounts, your music sounds not only colored, but distorted, like an overstressed AM radio speaker. This doesn’t happen in HiFi earphones unless you’re driving them at ear-splitting levels.

    The overwhelming reasons for why earphone FR plots are hard to interpret are,
    1. Lack of standardization in measuring equipment
    2. Lack of standardization in compensation curves
    3. Lack of standardization of human ears

    (1) and (3) both mean that the tonality difference between two earphones becomes a variable quantity, because different couplers and different ears will interact with different earphones differently. (2) is caused in part by (1) and (3), but it would have helped if we could have standardized on one pair of dummy ears, one compensation curve for it and stuck to it.

    Finally, an FR plot does tell me quite a bit about a pair of earphones’ soundstage, both via its general tilt at various frequencies, (e.g. elevated response at 3kHz and depressed response above 8kHz predicts better frontal imaging) and the smoothness or jaggedness of the treble response (a smooth response produces a clean, “studio”-like sound while a jagged response produces a grittier, more “live” sound). Also, for earphones with single drivers, the attack and decay speed at all frequencies can be calculated directly from the frequency response by assuming minimum phase response (which is almost always true in headphones). For earphones with multiple drivers, the crossover design impacts the final phase response, but not in an audible manner, except in circumstances of gross misdesign.

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