For example a computer sends an impulse signal or a frequency sweep to the equipment we wish to emulate and the impulse response or sweep response is recorded.
Same for emulating the reverb of a room.
In a few words the theory is:
Assuming a system is linear. In practice no system in nature is linear.
By the uncertainty principle in signals, the shorter a pulse the more bandwidth it contains.
A Fourier transform transforms from time domain to frequency domain. For example a sine wave looks like a sinewave in time domain. But in frequency domain it is just a point indicating the frequency.
A short duration sinewave is not a point in frequency domain as the shorter it is the more uncertain we are to its frequency. So in frequency domain it is curve with peak its frequency.
An impulse is a signal with infinite amplitude and infinitesimal duration so that it still has a finite area or energy in time domain.
The Fourier transform of the impulse is a straight line from minus infinite frequency to infinite frequency.
A realistic impulse approximation contains a large bandwidth. For example clapping hands once in front of a piano (this damper release pedal pressed) sets all strings of all available frequencies in sympathetic vibration. See Waves - Barkeley Physics Couse.
If the impulse output of a linear system is recorded and then the Fourier transform taken we receive the frequency response of the system.
The impulse response is unique for each system or characterizes it.
From it the behavior to any signal can be computed using the convolution theorem etc.
Is this a way plug ins operate?
Nice or ingenious as they may be they are not the real thing and consume energy.
It is great that plug ins are beginning to be used only when really needed.
For example why should one use a plug in to a mic chain when most of what is unwanted from a mic can be removed by connecting an inductor, or inductor capacitor combination, or inductor resistance combination. See RCA 77DX schematic, Electro-Voice RE-15 schematic, Shure SM7 schematic, EMI RS106A, Pleiades filter. They are all passive, no energy consuming, they just remove the signal energy that is not needed like photograohy filters. They can be directly connected to a mic getting rid of unwanted bass heaviness to listener's brain before it gets and compromises the rest of the analog stages. Wave filters can be balanced. [Elements of Sound Recording].
Why should one carry something unwanted even to the digital domain and not eliminate it at source? Plug ins are great. Why not giving them the best source signal?
Now a little on echo chambers.
They should be fun to make by converting an unwanted relatively small room. See for example Frank Laico interview on the Columbia church studio in New York and the small church store room used for reverb. Also installing drain pipes etc for diffusion as can be seen on BBC and Abbey Road studios photos, see references on other euroelectron posts.
Now a little on singing in tune. A singer should be in tune if the right sound acoustic intensity of the backing track is heard. See next euroelectron post. [Stevens], [Ramone].
Plug ins must be a great invention.
It is great that we are beginning using them rather than them using us.
Reference:
Introduction to System Dynamics - Shearer, Murphy, Richardson - Addison Wesley
Waves - Berkeley Physics Course, Vol.3
Anatomy of a Session - Frank Laico AES interview - YouTube
Sound and Hearing - S.S. Stevens, Warshofsky - Life Science Series
Making Records - Phil Ramone
Elements of Sound Recording - Frayne, Wolfe
Information Theory and Noise - Pettifer lectures at Warwick University Physics Department
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