Exactly what is FR response?

Wikipedia actually has a pretty good section on this:

http://en.wikipedia.org/wiki/Audio_system_measurements#Measurable_performance

Take a look

Jack

I'll toss this out here and let others run with it.. I don't have a lot of time now... but here's the idea:

A microphone picks up sound and converts it to an electrical signal. If you view a signal on a plot it looks like a wavy line. For example,

http://blogs.mathworks.com/seth/2009/01/30/mathworks-conversations-and-the-fft/

The job of audio equipment is to transfer that signal from one form to another without distorting it. A tape recorder puts that signal in a permanent form on a tape. A CD burner puts it on a CD. A CD player or DAC turns it back into an electrical signal. An amplifier attempts to make it larger (more powerful) without distorting it. A headphone changes it back into sound, hopefully without distorting it too much.

But none of these devices functions perfectly. They all distort the signal in some way.

The frequency response plot (*) is an attempt to characterize the way in which a device distorts the signal. See this FR plot of a microphone:

http://www.totalvenue.com.au/articles/microphones/microphones.html

It's based on this observation:

• play pure tones through a device and vary the frequency of the tones from very low to very high
• don't change the loudness of the tones
• in a perfect device the output tone will stay the same loudness
• but in an imperfect device, the output loudness will vary. Most obviously, at very low frequencies the output will drop to nothing. And at very high frequencies, too.
• Plot that variation and presto you have a FR plot

Now you might ask this: what good is characterizing the behavior with pure tones, seeing as music is made of complex signals?

Well in the 19th century a mathematician named Fourier made a remarkable discovery: if you know the FR of a device, you can predict its response to any signal.

That's right---run some pure tones through it, and presto you've just described its behavior for all time.

But there's a huge caveat: the device must have a certain property called linearity for this mathematical proof to hold. And no real device is linear. Nonetheless, most real devices are close enough that the FR plot is useful.

There's a lot more to say about how the FR corresponds to perception, but this is the basic theory.

(*) The wikipedia article describes FR as a range of a low number to a high number. That's a variation on the idea I'm describing here. I am describing the foundation of the theory so you have a deeper understanding of what those numbers mean.

Frequency Response is a representative curve with which you tell someone their headphones suck.

The frequency response of a system is the ratio of the output signal amplitude to the input signal amplitude.  The value of this ratio depends on the frequency, so the FR is a function of frequency.

In audio land, the objective is faithful reproduction of the original input signal.  Therefore, a flat frequency response of 0 dB--where the input and output magnitudes are the same--in the audible frequency range (20-20,000 Hz) is desired.  If the frequency response is not flat in the audible frequency range, then some sounds passing through will be amplified (if positive dB FR) or attenuated (if negative dB FR) relative to what the original at the input actually was.

Side note:  was Fourier really responsible for LTI system theory?  Who determined the relationship between the impulse response, transfer function, and the characterization of LTI systems?  I thought he was just attributed to the idea that some continuous and discontinuous periodic functions can be expressed as a sum of sinusoids (Fourier series), though the details of convergence weren't resolved until later.  Anyhow, the history of mathematical and engineering discoveries really isn't my forte, so I'll leave it at that...

Maybe I misspoke earlier.  The "goal" is actually sound reproduction that you enjoy, which may or may not be sound reproduction that strives to be 100% accurate and transparent.  However, your stated goal is for hi-fi, so that point is moot.  My previous statements would apply for your case.

That said, there is much more to headphones than simply the frequency response.  FR just gives you an idea of relative quantity of sound at different frequencies without telling you anything about the qualities of the sound.  One headphone with a rolled-off (negative dB FR) bass may have much less distortions than another with a flatter FR.  Other headphones may produce more distortions, but they might be distortions that are harder for humans to discern or even euphonic distortions that some listeners even prefer.  Human hearing is strange enough as it is.  For one example, the same volume sound at 40 Hz doesn't sound as loud as the same volume sound at 400 Hz or 4000 Hz.  (more info here: http://en.wikipedia.org/wiki/Fletcher%E2%80%93Munson_curves)

There is also the argument that, in fact, many recordings are poorly mastered.  It may be "up to them" to decide how the music they put out should sound, but there's no reason you can't tweak whatever you want if that's your desire.

Anyhow, you can always apply EQ if you are not satisfied with your headphone's FR.  Other facets of headphone sound reproduction cannot be so easily tweaked.

Quote:

Originally Posted by Sonic Atrocity 

Hmm, you see I want fidelity in my sound. I was originally considering the Ultrasone PRO 750s, 900s, and Hfi-780s but the frequency responses of those phones are far from flat. Is it not up to the producer/artist how my music will sound? Anything that isn't flat is essentially modified. Perhaps I am wrong. I am just learning and am doing my best to understand the ins and outs of audio. I believe that challenging some of the axioms may is one of the best steps towards understanding.

Just to throw a wrench into the works, and give you something to think about:

Do you know what the producer/artist was using to monitor the mastering (headphones/speakers?), and do you know the frequency response of their headphones/speakers? Is there any reason to assume they used something perfectly flat?

For that matter, what is flat to you? 0dB response at all frequencies, or equal loudness at all frequencies?

Don't be so sure

Realise I've pulled the thread off-topic, but I think the above posters have covered FR quite thoroughly, so...

I do live sound mixing from time to time, using the ER4S, reputedly one of the least coloured IEMs, and guess what? It sounds nothing like the speakers I'm broadcasting through. It's been said the ER4S is good for revealing bad things about mixes, and so it should be for any monitor if you want to create a good mix. However, if the main speakers sounded anything like the ER4S, it'd end up driving people away from the event.

A sound that is mostly equal loudness at all frequencies (Fletcher-Munson curves, as pointed out by mikeaj), perhaps with more bass and less treble emphasis, is generally more pleasing and easier to listen to, for the man on the street; it's no accident that most mass-market earphones and headphones out there have such a sound (not to mention that a 0dB-response driver probably requires a lot of engineering and power).

One of the rules of thumb for mix/mastering engineers is that they should monitor the mix with [something] that sounds close to what their intended audience would be using. If it sounds good out of [something], it's then more likely that it'll sound good for the final audience. Hint: very few recordings are targeted exclusively at flat-FR audiophiles

Quote:

Originally Posted by Sonic Atrocity 

Oh, how come Sir?:P

See above post.   Flat isn't exactly what you think.

But hey, it could be 'your' sound, no way to find out but to try.
 

Quote:

Originally Posted by radioactive28 

A sound that is mostly equal loudness at all frequencies (Fletcher-Munson curves, as pointed out by mikeaj), perhaps with more bass and less treble emphasis, is generally more pleasing and easier to listen to, for the man on the street; it's no accident that most mass-market earphones and headphones out there have such a sound (not to mention that a 0dB-response driver probably requires a lot of engineering and power).

 

Could you clarify this, because in acoustic music (at least) the Fletcher-Munson curve isn't related to the FR---it's related to what the musicians do. That's why tubas put out so much energy. That's why they have several basses in the orchestra. You need bass power to make balance. The musicians aim for balance as heard by an observer standing right there.

Quote:

Originally Posted by mike1127 

Could you clarify this, because in acoustic music (at least) the Fletcher-Munson curve isn't related to the FR---it's related to what the musicians do. That's why tubas put out so much energy. That's why they have several basses in the orchestra. You need bass power to make balance. The musicians aim for balance as heard by an observer standing right there.

 

I meant to point out that a perceived 'flat' response (equal loudness) is more natural-sounding, and therefore more balanced, to the average person than a 0dB-flat response. This would drive manufacturers to make earphones/headphones with a FR that resembles the shape of the Fletcher-Munson curve(s).

I'm not a musician, and most of what I know is self-taught, so please point me out if something is grossly wrong.