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The frequency sweep is how it's made; you play a sign wave sweep through the system and record the response.
Originally Posted by rpjazzguitar
I won't pretend to be an expert on convolution (lol), but my understanding is this:
A simple EQ is just addition and subtraction. If you have a 3db cut at 1000 hz, the amplitude at 1000hz in the input signal is cut by 3db, regardless of the frequency content of that signal.
A convolution is multiplying the amplitude of the frequency content of the input by the amplitude of the frequency response of the IR to arrive at the frequency output. So now the output is dependent on the interaction of the input and the "filter" in a way that isn't the case for a static, linear EQ.
Regarding OPs point about the interaction between amp and speaker, it's not necessarily required to directly model that interaction to correctly capture the response of the interaction. This is analogous to the different types of amp modelling approaches. If I understand correctly, the Kemper algorithm is capturing the response of an amplifier rather than modeling the components, whereas I believe the axe fx is the other way around.
Which isn't to say there aren't things that IRs don't capture, but I think it's more complicated than just saying an IR is "static" and therefore can't replicate a "dynamic" system.
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01-19-2024 03:38 PM
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Thank you. This gets to the heart of the matter. Originally Posted by BreckerFan
In making the IR, the frequency content of the input is the impulse -- sweeping a sine wave through all the frequencies. Is that much correct? Would that be the same as basically a flat line - frequency on the X axis and amplitude on the Y axis (with all amplitudes being the same)?
The frequency content of the output is, presumably (I might be wrong on this) another graph, in essence, again, frequency vs amplitude.
The convolution process divides up the frequency spectrum of the output into a zillion slices and does a simple division for each one. X (for each frequency) = output amplitude/input amplitude. Then, you assemble all the zillion X's into a curve and that's the IR.
If this much is correct, than the IR basically, figures out what some classic amp does to the frequency spectrum and duplicates it.
What have I missed or misunderstood?
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In my understanding this is basically correct yes. The capture process is done just by taking an audio recording of the sine sweep through the setup, so just amplitude vs t, which is why the typical IR format is a .wav file. Then in the convolution process, through the magic of Fourier transforms it is converted to amplitude vs frequency. Originally Posted by rpjazzguitar
I would also guess that rather than dividing input v output they are subtracted from each other so that you get a function of change in amplitude vs t/f rather than a ratio of the two.
Also important to note that making an IR for an amp is difficult to impossible, especially the more clipping is included, because I don't think IRs can capture non-linear response. I've used some clean amp IRs that are ok though somewhat lifeless. But since a speaker/mic is basically linear at most useable volumes, it works.
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Great stuff. Would be nice to have a better understanding of the tech.
- Given the process that doesn't change much, mic's are similar, positions are similar, rooms are controlled, why are some IR's good and some not-so-good?
- IR's should be fairly frequency constrained given the source. Some are even intentionally cut off at 5Khz. So why do they sound better with high fidelity speakers and not good with a simple guitar cabinet? Thinking it's the transient response but still curious about it.
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Because the guitar cab is designed go add its own color so your basically mixing blue with yellow and asking why it turned green. Originally Posted by Spook410
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Sine sweep
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how to make an IR - Google Search
This video explains what an IR is and how it's made. You need a mic, a DAW and the rig you want to model.
It's basically a recording of white noise played through a particular device, e.g. an amp. You play the white noise into your amp and record the result with a microphone into a DAW. Then, apparently, you clip a piece of it and normalize (basic edited stuff in a DAW like Reaper or Protools) and that's the IR. Apparently the DAW software knows how to apply it to your next recording - I'm not clear on that part of it.
But, it amounts to a graph of frequency vs amplitude, if I understand it correctly.
So, it varies with the equipment you use to make it.
I don't know how it would be different than a hypothetical graphic EQ with a very large number of bands.
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That’s my jam Originally Posted by Bop Head
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For speaker cabinets I think using a sin wave is typical as opposed to white noise. And I don't think convolution is the same thing as normalization in a DAW which seems to be a much simpler kind of signal processing. There was a time in my long lost youth while I was at university getting my engineering degree I could have dug into this. Now.. not so much. Originally Posted by rpjazzguitar
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Speaking again about something I know nothing about ... If somewhat similar to what is used in regulation systems then the IR handling should provide two curves in frequency domain. One for amplitude and one for phase. So there is a difference to the multichannel equaliser. Originally Posted by rpjazzguitar
Also the length/number of points in the input file may have an influence on how much ambience/dynamic can be represented. It is thechnically interesting. Maybe I should read up a bit on this.
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I’m still a bit unclear folks ….
do any of these IRs ,however derived
measure the system response at many different levels (volumes quiet medium loud) ?
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No, they are a static snapshop of a certain state. Originally Posted by pingu
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Let me see if I get this.. Originally Posted by Bop Head
- The input is known. A simple sin wave of known amplitude (volume) and known frequency (from 20hz to 20Khz swept across a specific time interval).
- The speaker and cabinet is known
- The mic and it's position is known
- What is measured is how the speaker responds in the cabinet and in the room. As measured by the mic.
- The measurement and the sin wave input are mathematically combined (convolution) to identify the unique characteristics of the speaker/cabinet/room per that specific measurement tool (mic/placement) in that specific space
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In the video, the IR was made with white noise at one volume level. I don't know if that's the only way to do it. Originally Posted by pingu
Done the way shown in the video, the IR is a short piece of the recording of white noise played through the physical amp/speaker/cab/mic.
What I see on my DAW screen (not the one in the video) when I look at a wave form is amplitude vs time. When I play it back, obviously I'm hearing frequency information.
Seems to me that the IR is, if I understand it, the graph of frequency vs amplitude at a moment in time.
Then, when you play a new recording through that IR, it adjusts every frequency in accordance with that graph. I don't know the math of how that's done. I'd guess that each frequency (for however many slices of frequency are being used) is labeled with a measure of deviation from a norm, expressed perhaps as a ratio from a baseline, and then the new recording is adjusted, for the same frequency bands, by the same ratios. An earlier suggestion was that it might be additive, but I can't quite think that through.
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I think that video was for a 'do it yourself' with commonly available tools. Get the impression that commercial IR's are made with sin wave sweeps and special convolution tools. Don't think an IR is a white noise recording that been trimmed and normalized. Not sure why the latter even works but then again I don't know what a DAW is looking for when you tell it to use something you've designated as a speaker cabinet. Originally Posted by rpjazzguitar
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Sine wave sweep contains every frequency and so does white noise. So, I guess, the same basic info is contained in each. The data is frequency and amplitude and, maybe time. It may be that time is reduced to a snapshot of frequency and amplitude. Originally Posted by Spook410
I read, just now in Wiki, that a standard EQ approach can approximate an IR, if you have enough frequency bands, I guess.
I still don't understand how it deals with phase, clipping or time-transients.
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There is a huge difference. A sine sweep "plays" a specific frequency at a certain point in time. White noise is all frequencies at once. Originally Posted by rpjazzguitar
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I think that the wav file is processed by figuring out what the amplitude is for each frequency. I'd guess that you can divide white noise, or a sine sweep, by frequency and find the amplitude of each. More accurately, you divide the frequency spectrum into a large number of tiny bands and get the amplitude for each. Originally Posted by Bop Head
In the case of sine sweep, the frequencies are in order. In the case of white noise they're random. But, in either case, they're all there.
Or, so I think today. I'm just trying to figure it out.
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I give up. Too much guesswork ...
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My guess is that generating an IR from a burst of white noise may not be very useful.
This site explain things quite well Impulse responses (IR) - Fractal Audio Wiki (to anyone having a little spare time to read)
They also explain a little about the role of the length and resolution of the recorded impulse response mentioned above.
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All of this is prefaced with it being according to my understanding. I'm an engineer by day, but not this kind of engineer, and so I won't garuntee that it's all perfectly accurate lol.
-time and frequency are inversely related to each other. Frequency is the measure of cycles per unit of time (Hz is cycles per second), with a cycle being one complete sine wave (one crest and one trough). But you can also measure the time it takes for one cycle to complete, which gives you the period. If you know the period you can get the frequency via T = 1/f and vice versa.
-Any waveform (amplitude vs time) can be thought of as the sum of a number of sine waves of different frequency. Literally, by adding up sine waves of the right frequencies and amplitudes, through phasing, you can produce any sound. Conversely, you can decompose any wave into its component sine waves. This is done using the Fourier transform. If you take the Fourier transform of an amplitude vs time wave, the output is an amplitude vs frequency graph (as well as information about the phase of the component waves).
-The Fourier transform is used in many ways in computing, using a special type called the Fast Fourier transform. This allows in our case an audio signal to be quickly processed from the time domain to the frequency domain and back again with minimal latency (milliseconds). Digital EQs use this.
-A digital EQ will FFT a signal into amplitude vs frequency and then add or subtract to the amplitudes of the selected frequencies, and then inverse FFT the new plot back to time vs frequency for output.
-convolution/IR is different. You start with two amplitude vs time waveforms, your guitar/amp signal and the sine sweep of your speaker/mic. You want to process the guitar/amp signal through the speaker/mic signal. Convolution is a mathematical operation the processes the shape of one function through the shape of another function. When considered in the time domain it's an ugly integral, but for math reasons (above my paygrade lol) a convolution of two time functions can be performed by taking the fourier transform of each and multiplying the amplitude vs frequency plots together. You then inverse Fourier transform back to the time domain and you have your processed signal.
-you can see how an IR is different than an EQ. An EQ applies a fixed addition or subtraction to your waveform, regardless of the frequency content of your input. In convolution, the output is dependent on the input frequency content in a way that it isn't for an EQ. You couldn't just take a multiband EQ and apply a bunch of cuts and boosts, because that is just performing addition and subtraction, not multiplying the frequency content as in convolution. In this way an IR would be more "dynamic" than an EQ because the amount of boost and cut varries with your input.
-The "dynamics" that an IR can't capture are non-linearities (clipping, compression, etc.) Compression says input = output up to a certain level, beyond which output increases at a rate less than input. Clipping is the same thing but with a hard limit rather than just a reduction. An IR can't capture this because it's only taking one data point. You have your input at a certain amplitude and you get your output, and you can find the difference between them. But you aren't measuring how this change varies at different input amplitudes.
-this is ok for a speaker/mic setup, because the non-linearities that occur in a guitar amp generally occur in the pre and power amps, not the speaker. The speaker is linear unless you're pushing it so hard that it's breaking up, but that's kind of it's own sound and especially atypical for jazzers lol. So IRs are only made of the cabinet and mic, not the full amp/cabinet system. You still have to use a power amp of some kind to push the sine sweep through the cabinet, so you want to use something clean, linear, and flat to capture the speaker response as accurately as possible.
-a sine sweep and white noise can both be used, but I think a sine sweep is better because you can distinguish the response at each frequency more clearly since it isn't all occuring simultaneously.
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FWIW: I remember Thomas Blug of Amp1/AmpX talking about their development of some kind of dynamic IRs for their soon to be released AmpX.
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Thank you for taking the time to explain all of this. Originally Posted by BreckerFan
Speaking conceptually, trying to get the gist of it ...
We play some white noise or a sine sweep through an amp, cab and mic. We look at a short clip of the recording. At any instant there's an amplitude. If you take a short slice of time, you can detect frequency (variation in amplitude over time; how much time depends on the frequency). Fourier transform gives a series of component sine waves, which are all present at the same time.
The convolution is done numerically, starting with this clip. It has amplitude, frequency and time. And, if I understand it, the arithmetic is done a slice at a time. For that slice, what does the math look like?
Or is that even a well-posed question?
When a programmer writes a program to do this, what variables are being manipulated at the granular level?
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Originally Posted by BreckerFan
Excellent. That was a lot of work to write up but it cleared some things up for me. Thank you BreckerFan.
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Normally when playing back a digitized guitar signal, the D2A converter replaces each sample with an analog impulse having the same height but of a particular shape. The shape (sin(x)/x) is chosen so that these impulses add up to exactly reproduce the analog waveform.
The impulse response or IR file consists of a long string of values at the same sample rate as the guitar signal.
When the IR is used, each individual guitar signal sample is replaced by a string of samples equal to the original times the contents of the whole IR. Because the sample rates are the same, this string will be in step with the continuing guitar signal. These new strings of samples are all added together to produce a new waveform for output. This process is called convolution. You end up with a whole series of (IR*sample) added together, each one offset by one sample period from the previous one. This new string of samples goes to the D2A converter.
The way the math works out, the whole process acts like a digital filter that represents the frequency response of the source of the IR from a low frequency, determined by the length of the IR, up to half the sample rate.
The IR filter can represent the fine detail in the frequency response of a speaker, including internal reflections and the cone breakup at a particular sound level. It is purely linear and cannot represent distortion.
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