I am poor at math, but I believe that "wavefront induced by a line array" is a diffuse concept, when we discuss music reproduction - because of wide variation of wavelengths causing a multitude of interferences in vertical dimension (along the line)
But anyway, the sound perceived is very natural and lifelike, pleasant. A point source like synergy horn gives totally different wavefront and different clear sound/imaging, which many people like even more.
But anyway, the sound perceived is very natural and lifelike, pleasant. A point source like synergy horn gives totally different wavefront and different clear sound/imaging, which many people like even more.
POST #5
2. Point Source: time-domain impulse response (continued)
Let the INPUT of an LTI system be the impulse function :
x(t) = delta(t)
Let's define the OUTPUT to be the time-domain "impulse response", h(t). How do we find it?
Simple! We take the Inverse Fourier Transform of the system's frequency-domain "transfer function"
(this really follows directly from the convolution integral, and the definition of the Fourier Transform).
Sometimes ... the best way to take an "inverse" Fourier Transform, is just by recognizing a common Fourier Transform. The definition of the Fourier Transform is :
H(jw) = int[h(t)*exp(-jwt)]dt
An example : Let's say (just for the hell of it) that the system responds to an impulse with a very simple time-delay ... so that the impulse response is:
h(t) = delta(t - Td)
Where Td is the system's time delay.
What would such a system's "transfer function" be? Glad you asked ...
H(jw) = int[delta(t - Td)*exp(-jwt)]dt
H(jw) = int[exp(-jwTd)*delta(t - Td)]dt
H(jw) = exp(-jwTd)*int[delta(t - Td)]dt
H(jw) = exp(-jwTd)
aha! we've just identified a quite common, and very useful "Fourier Transform Pair" :
h(t) = delta(t - Td) <----> H(jw) = exp(-jwTd)
Recalling the mag & phase properties of the so-called "transfer function", we see that a simple time delay corresponds to a transfer function with unity magnitude and linear phase (corresponding to the time delay, Td).
Now we have all we need (finally!) to derive the (now, rather trivial) time-domain impulse response for our little point source radiator ...
2. Point Source: time-domain impulse response (continued)
Let the INPUT of an LTI system be the impulse function :
x(t) = delta(t)
Let's define the OUTPUT to be the time-domain "impulse response", h(t). How do we find it?
Simple! We take the Inverse Fourier Transform of the system's frequency-domain "transfer function"
(this really follows directly from the convolution integral, and the definition of the Fourier Transform).Sometimes ... the best way to take an "inverse" Fourier Transform, is just by recognizing a common Fourier Transform. The definition of the Fourier Transform is :
H(jw) = int[h(t)*exp(-jwt)]dt
An example : Let's say (just for the hell of it
) that the system responds to an impulse with a very simple time-delay ... so that the impulse response is:h(t) = delta(t - Td)
Where Td is the system's time delay.
What would such a system's "transfer function" be? Glad you asked ...
H(jw) = int[delta(t - Td)*exp(-jwt)]dt
H(jw) = int[exp(-jwTd)*delta(t - Td)]dt
H(jw) = exp(-jwTd)*int[delta(t - Td)]dt
H(jw) = exp(-jwTd)
aha! we've just identified a quite common, and very useful "Fourier Transform Pair" :
h(t) = delta(t - Td) <----> H(jw) = exp(-jwTd)
Recalling the mag & phase properties of the so-called "transfer function", we see that a simple time delay corresponds to a transfer function with unity magnitude and linear phase (corresponding to the time delay, Td).
Now we have all we need (finally!) to derive the (now, rather trivial) time-domain impulse response for our little point source radiator ...
POST #6
2. POINT SOURCE: time-domain impulse response (continued)
We've identified the frequency-domain "transfer function" of our simple little point source to be :
H(jw) = {(rho)/(4pi*r)}*{exp(jwTd)}
From the nifty Fourier Transform Pair that we recently uncovered, we can immediately write the time-domain impulse response for the point source radiator :
h(t) = {(rho)/(4pi*r)}*{delta(t - Td)}
That's it !!
What does it mean?
If the excitation of our little point source is a classic "impulse", the response measured at any point in space is simply a delayed impulse, attenuated in magnitude by 1/r (where r is the distance from the source). It's really fair to describe this scenario as a "faithful spherical radiation", i think. Not only do we measure the pressure to be the same at any point on a sphere with radius "r" (due to simple symmetry), but the impulsive 'character' of the original "impulse" is preserved as well, at any point in space.
And that about wraps it up, for the "elemental monopole" Point Source We started here, in preparation for the Infinite Line Source, to establish both a terminology (in engineer lingo) and a methodology. Might be about a week before i can return to move things forward (cuz the holiday), but it's a good time for more discussion, i think thanks for your continued indulgence, my friends!
2. POINT SOURCE: time-domain impulse response (continued)
We've identified the frequency-domain "transfer function" of our simple little point source to be :
H(jw) = {(rho)/(4pi*r)}*{exp(jwTd)}
From the nifty Fourier Transform Pair that we recently uncovered, we can immediately write the time-domain impulse response for the point source radiator :
h(t) = {(rho)/(4pi*r)}*{delta(t - Td)}
That's it !!
What does it mean?
If the excitation of our little point source is a classic "impulse", the response measured at any point in space is simply a delayed impulse, attenuated in magnitude by 1/r (where r is the distance from the source). It's really fair to describe this scenario as a "faithful spherical radiation", i think. Not only do we measure the pressure to be the same at any point on a sphere with radius "r" (due to simple symmetry), but the impulsive 'character' of the original "impulse" is preserved as well, at any point in space.
And that about wraps it up, for the "elemental monopole" Point Source
We started here, in preparation for the Infinite Line Source, to establish both a terminology (in engineer lingo) and a methodology. Might be about a week before i can return to move things forward (cuz the holiday), but it's a good time for more discussion, i think thanks for your continued indulgence, my friends!
Thoughtful, informative stuff
A few thoughts on "height" ...
- "Height" is mainly perceived by the shape of our outer ears (absent them, our heads are almost spherical with holes in the sides, with a resultant symmetry that would make height detection almost impossible). The dimensions of our outer ears restrict height cues to the frequency range above about 3~4kHz.
- I love, admire and respect classic stereo (and Blumlein, the man who invented it) ... but let's face it, it's a terrible medium for capturing and replaying height information with any real fidelity ... at least, based on my knowledge and experience.
- An Infinite Line Array will indeed be presenting the same signal, to a listener, from a elevation angle range spanning +/- 90 degrees. It's absolutely true that a variety of HRTF's will be "in play". The resulting signal presented to the eardrum will be that signal resulting from, essentially, an "average" HRTF ... it's simply a signal presented through a "parallel array" of transfer functions, before reaching its final destination. I *suspect* that the ear/brain will integrate this info and "assign", if you will, a "height" that "makes sense", corresponding to the rest of the frequency range plus our experience as humans. Remember, we're only talking about the treble here ...
My educated guess (education based on some knowledge, and some experience with line arrays) is that the only downside to the apparent "height ambiguity" associated with very tall (maybe infinite) lines is this : as we move from a seated to a standing position, whatever "height" we perceive ... whatever "height" our brains have trained themselves to perceive ... will move upwards with us. A bit un-natural, perhaps
but not ultra-critical.i hope others with experience with chime in !!!
People turn their heads often without even being aware they are doing it. Resulting variations in sound arriving at the eardrums are used by System 1 brain processing to help estimate the direction sound is coming from. Static HRTF clues are usually augmented by motion, often considerably so.
i've heard several large scale arrays (sound reinforcement) properly focused and arrayed (as in a j hang) they don't seem to appear "taller".
time alignment is critical though.
HRTF's are an interesting topic but more applicable to binaural recording. not sure how they apply in this instance?
time alignment is critical though.
HRTF's are an interesting topic but more applicable to binaural recording. not sure how they apply in this instance?
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My educated guess (education based on some knowledge, and some experience with line arrays) is that the only downside to the apparent "height ambiguity" associated with very tall (maybe infinite) lines is this : as we move from a seated to a standing position, whatever "height" we perceive ... whatever "height" our brains have trained themselves to perceive ... will move upwards with us. A bit un-natural, perhaps
i hope others with experience with chime in !!!
I can confirm this behaviour for my arrays. If I stand up, the perceived stage moves up with me. It's a bit weird the first time. No changes in the perceived tonal balance.
With FIR correction applied I never experienced unusual "tall images".
I have noticed this same "climbing" of sound source with Acoustat panels (not heard Quads, Magnepans or Martin Logans). A bit strange but not annoying. Neither have I heard tall line arrays in nearfield sorry, but I believe that this happens with them too.
While being in one position with Acoustats, different treble sounds come from different height, this is funny at first, but that is how they appear in a concert hall with live acoustic music too. I guess that this is because of different frequencies having different paths of reflections or just different status of combing. Sometimes a small movement of head moves the apparent sound source. This doesn't happen with conventional speakers or even with my 4-way dipoles in this magnitude.
While being in one position with Acoustats, different treble sounds come from different height, this is funny at first, but that is how they appear in a concert hall with live acoustic music too. I guess that this is because of different frequencies having different paths of reflections or just different status of combing. Sometimes a small movement of head moves the apparent sound source. This doesn't happen with conventional speakers or even with my 4-way dipoles in this magnitude.
And I can confirm that is what happens with arrays also. The images moves up when standing but the tonal balance remains the same. We recently had a movie night and many of us sat on the floor. It is good that you can clearly hear dialogue sitting down on the floor and pretty much everywhere in the room. The moving images help a lot in localization.
I did not experience anything like this with my arrays. Just to be clear about it.
If I stand up, the imaging/virtual stage seems to move up with me. No high frequencies that seem to come from higher places etc.
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