Source
r/audioengineering•
ReasonHead

Transient response vs frequency response

I was reading an article on ribbon mics and foil thickness and the author said that thinner foils don't give the ribbon mic more high frequencies but "better quality high end" and "better transient response". Isn't more accurate transient response the same as less high frequency roll-off? Or does transient response differ a lot through narrow peaks/valleys in the high end of the frequency response that are being smoothed in normal frequency response plots which thinner foils improve on?

Posted Feb 13, 2020, 10:02 AM UTC

2934
OnAGoodDayMixing•

Transient response is the way the system reacts to changes from equilibrium like a step or impulse. It's characterized by metrics like rise time (from a step), overshoot (step), settling time, etc. These are all dependant on damping, spring constant, and mass. I'm an EE so I can't remember exactly how they all work but damping, springyness, and mass are mathematically equivalent to resistance, inductance, and capacitance, respectively. You can actually create a mechanical "circuit" and solve it, or find the frequency response this way.

Anywayyyy, you get what's called a characteristic equation (i.e. the differential equation smooshed into the Laplace domain, which makes it easier to work with) with damping, spring constant, and mass; and I believe you can calculate the dynamic response characteristics or at least simulate it, and you can definitely draw a Bode plot or simulate a sweep or impulse to give you frequency response.

So, from the same equation you can calculate or simulate both dynamic response and frequency response. They are two ways of looking at the same thing, each which give you a new insight to the system's behaviour.

14
Chaos_Klaus•

Well, transient response will include things like ringing, ect. So it's not the same as frequency response. But it's closely related and a thinner diaphragm definitely has less high frequency roll off.

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StacDnaStoob•

For LTI systems (which is a close enough approximation if the mic isn't distorting), ringing can be determined from frequency response.

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Chaos_Klaus•

My intuition was that it's not LTI ... but that was just a guess based on transient responses of speakers with bass reflex ports.

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jpdoctor•

If it's not LTI, then knowing the transient response is also not very useful, unless you plan to record signals that are approximately the same impulse with the same energy, since there will be a nonlinear change in response with a change in the excitation impulse.

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ReasonHeadOP•

So less ringing also means better transient response because it implies less inertia and therefore less mass?

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ThickAsABrickJTAudio Hardware•

Sort of. Less ringing does mean better transient response because ringing is a "bad" thing that can happen during transients.

Less ringing implies greater damping, which is a function of mass, air resistance (determined by diaphragm area), and spring constant (determined by how tightly sprung the ribbon is). The exact relation is some obnoxious differential equation that I don't remember off the top of my head right now.

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h3nni•

Transient Response and Frequency Response are different ways to describe the same thing and can be converted into each other.

5
munificent•

My understanding is that this is only true when you have the complex frequency response with both magnitude and phase. But often when people casually talk about "frequency response", they only consider magnitude. The phase response can significantly affect how well transients are preserved. This is why "minimum phase" filters and EQs are a thing. They help preserve transients better.

Here's a thought experiment that should help visualize it. Imagine taking a square wave. It will have very nice, sharp transients. Now takes its frequency response and completely randomize the phases of each frequency. From that, reconstruct the time domain signal. It will look nothing like a square wave and the transients will get smeared all over the place, but it will have the exact same frequency response magnitudes.

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jpdoctor•

My understanding is that this is only true when you have the complex frequency response with both magnitude and phase.

Given the magnitude over a sufficiently wide range of frequency, you can determine the phase (although it requires a fairly high level of complex analysis to understand why.) It's certainly an easier calculation if you have the phase though.

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[deleted]•

How so? Just curious.

2
TizardPaperclip•

It seems to me that the transient response measures the amount of time it takes the diaphragm to react to an impulse (say, 50 microseconds).

If that's the case, then the maximum frequency it could accurately respond to would be 20 kHz (1 divided by 50 microseconds).

So they should be inversely proportional.

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gainstagerAudio Software•

Devils advocate and honest question: this would go out the window as soon as it’s any longer than an impulse though, right?

In the 20kHz example, as long as say a 40kHz tone is played for the same amount of time, forgoing any technical limitations, it would be represented as well?

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TizardPaperclip•

At 40kHz the diaphragm would bounce and flutter around due to resonance. I don't know enough about microphones to guess what sort of waveform it would generate.

I imagine it would look a bit like two people trying to swing a skipping rope too fast.

3
ReasonHeadOP•

It seems to me that the transient response measures the amount of time it takes the diaphragm to react to an impulse (say, 50 microseconds).

If that's the case, then the maximum frequency it could accurately respond to would be 20 kHz (1 divided by 50 microseconds).

The theory is that you have an impulse that is infinitely small and let the microphone react to that. By the response to the impulse you can measure an arbitrary amount in frequency precision (width of frequency bins) and frequency, the former increasing with how much of the response you measure and the latter increasing with the sample rate you use to record the measurement. "Arbitrary" amount is limited, though, by accuracy of measurement devices and the accuracy of the impulse you can provide to the microphone (creating a very short impulse is rather difficult in practice).

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h3nni•

Laplace Transform, only for linear time invariant systems

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jpdoctor•

If it's not a linear time invariant system, then the impulse response is also pretty useless, unless you are planning to measure only impulses like the one measured.

1
helloiamnice•

They are the same thing, just exist in different domains. The transient response exists in the time domain while the frequency response exists in the frequency domain. You can take the transient response in and out of the frequency domain with a Fourier transform or inverse Fourier transform respectively.

A “cleaner” transient response might have less distortion and clipping, which would mean less harmonics in the frequency domain. Or maybe it would have less ringing, which would mean a flatter response in the frequency domain.

I hope this helps!

Edit: I’ll add that the impulse response is what you use to get the frequency response. If you have a step response (I assume what you meant by transient response) you can get the impulse response by taking the derivative of it.

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oDrori•

Basically this, although the term transient response should more accurately be called impulse response

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bobbooo888•

Isn't that all predicated on the assumption that it's a perfectly minimum-phase system though?

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helloiamnice•

This is just the way the math works out, I don’t think there’s any assumption it’s a perfectly minimum phase system.

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sowrAudio Software•

Many answers here are misleading or wrong. The impulse response is what can be converted to the frequency response and vice versa. The transient response is how a system reacts in the time domain to a step function.

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ReasonHeadOP•

Right, transient would be step, rather than impulse. The step response also contains all the info, though, right? So I could get the frequency response from the step response if I wanted.

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sowrAudio Software•

You would have to subtract a single sample delayed transient response to get the impulse response since the impulse delta(n)=u(n)-u(n-1) where u is the step fcn and n is the sample index

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ReasonHeadOP•

That's right, good point! But knowing the input function (a step function) couldn't you (with some other, specialized function) directly get the frequency response? I think I've read somewhere that the actual input signal is not relevant you just have to know what it is and that an impulse is just the most convenient/straight forward. Kinda like you can get the impulse response from a sine sweep with deconvolution.

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sowrAudio Software•

Right. For a linear system h, you can convolve with the step fcn h * u. So, the impulse response h(n) = h * delta(n) = h * u(n) - h * u(n-1) where * denotes convolution.

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helloiamnice•

The impulse response is the derivative of the step response.

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sowrAudio Software•

But naively looking at the fourier transform of the step response will not be the same as the FT of the frequency response.

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jpdoctor•

Many answers here are misleading or wrong. The impulse response is what can be converted to the frequency response and vice versa. The transient response is how a system reacts in the time domain to a step function.

Not wrong really, just different: The step response gives you the Laplace frequency response of the system, and the impulse gives you the Fourier frequency response of the system.

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sowrAudio Software•

Expand on this, because it does not sound right. The Laplace transform is the convolution with the fcn exp(s*t) where s is complex, and all you have to do to get the FT is set s = i*2*pi*f. You can apply the Laplace transform to either the impulse response or the step response, but they will be different.

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jpdoctor•

Take a look at the mathematical definitions:

You mentioned the change in variable of s to -i2pi*f, you didn't mention the difference in the limits of integration. So aside from some factors of i showing up differently between the two, the very meaning of the transform changes as well, which is why Laplace gives you the step response and Fourier gives you the impulse response in a natural way.

There are other consequences as well (like what constitutes a causal signal), but that gets deeper into the weeds of complex analysis.

1
Simtau•

I don't know for sure but I can imagine that transients can be significantly higher in level than the rest of the signal. This may cause distortion which may change the character of a sound. So lots of distortion in transients may be a bad transient response. I'm just guessing. Maybe somebody who knows more about it can say more about it?

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[deleted]•

[deleted]

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