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scott <sco### [at] scott com> wrote:
> > (Btw, did you know that even if a sound signal has only one single
> > frequency, a discrete fourier transform is usually completely unable
> > to find that single frequency, and instead will find a large (potentially
> > infinite) amount of frequencies around that real frequency?)
> It just depends how many samples you use for your fourier transform, the
> more samples you take, the more accurately you can divide up the frequency
> spectrum. If you have a couple of seconds of normal audio recording (so
> like 100k samples), you should be able to find a single frequency pretty
> accurately, certainly to within 1 Hz.
If the actual frequency falls in between two frequencies of the DFT,
there's no way for the DFT to produce just one or a few lines. Only if
the frequency happens to be exactly on one of the frequencies sampled
by the DFT, it will generate one single line.
--
- Warp
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Orchid XP v8 wrote:
> More significantly, if the same frequency is present in more than one
> channel, phase will matter.
I think phase matters for mentally positioning the source of a sound,
too. I'm pretty sure that's one of the ways they make those "surround
sound headphones" and those "sounds like you're there" recordings.
--
Darren New / San Diego, CA, USA (PST)
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Darren New wrote:
> Orchid XP v8 wrote:
>> More significantly, if the same frequency is present in more than one
>> channel, phase will matter.
>
> I think phase matters for mentally positioning the source of a sound,
> too. I'm pretty sure that's one of the ways they make those "surround
> sound headphones" and those "sounds like you're there" recordings.
Oh, sure. But if you want that level of sound clarity, you're using
lossy audio compression...why? ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
> Oh, sure. But if you want that level of sound clarity, you're using
> lossy audio compression...why? ;-)
Just saying....
--
Darren New / San Diego, CA, USA (PST)
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On Tue, 04 Nov 2008 19:17:50 +0000, Orchid XP v8 wrote:
> Stephen wrote:
>
>> Why are we here?
>
> We're bored?
>
>> What is the meaning of 42?
>
> Would it be wrong to reply "4 * 10^2 + 2 * 10^2"? ;-)
Yes, because you've just described the number 600. ;-)
Jim
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> If the actual frequency falls in between two frequencies of the DFT,
> there's no way for the DFT to produce just one or a few lines.
Of course there is, try it. If you create a frequency that is half-way
between two frequencies in the DFT, your DFT histogram will still look the
same shape, the peak will just be shared between the two frequencies.
And of course if you analyse the DFT properly (ie not just look at a picture
of the magnitude of each result) you will be able to determine the exact
frequency. I mean in the worst case you can just do an inverse DFT to get
back the exact same signal!
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scott wrote:
>> (Btw, did you know that even if a sound signal has only one single
>> frequency, a discrete fourier transform is usually completely unable
>> to find that single frequency, and instead will find a large (potentially
>> infinite) amount of frequencies around that real frequency?)
>
> It just depends how many samples you use for your fourier transform, the
> more samples you take, the more accurately you can divide up the
> frequency spectrum. If you have a couple of seconds of normal audio
> recording (so like 100k samples), you should be able to find a single
> frequency pretty accurately, certainly to within 1 Hz.
IIRC, there's a version of the Fourier transform from a discrete time
domain to a continuous frequency domain. Anybody know details?
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scott <sco### [at] scottcom> wrote:
> Of course there is, try it. If you create a frequency that is half-way
> between two frequencies in the DFT, your DFT histogram will still look the
> same shape, the peak will just be shared between the two frequencies.
The same shape as what?
Basically you are saying that you can recreate a sine wave (which is one
single frequency) with the sum of two sine waves (the two frequencies in
the discrete frequency spectrum)? Not only that, but the two sine waves
in question are adjacent to each other in the discrete frequency spectrum?
I would be interested in seeing some simple math about this.
--
- Warp
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>> Of course there is, try it. If you create a frequency that is half-way
>> between two frequencies in the DFT, your DFT histogram will still look
>> the
>> same shape, the peak will just be shared between the two frequencies.
>
> The same shape as what?
As a frequency that is exactly lined up with one of the bands of the DFT.
> Basically you are saying that you can recreate a sine wave (which is one
> single frequency) with the sum of two sine waves (the two frequencies in
> the discrete frequency spectrum)?
No, I am saying that given a finite DFT transform result with more than one
non-zero entry, if you perform the inverse DFT you will recreate a single
frequency sine wave.
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Warp wrote:
> Basically you are saying that you can recreate a sine wave (which is one
> single frequency) with the sum of two sine waves (the two frequencies in
> the discrete frequency spectrum)? Not only that, but the two sine waves
> in question are adjacent to each other in the discrete frequency spectrum?
>
> I would be interested in seeing some simple math about this.
sin x + sin y = 2 cos (x-y)/2 sin (x+y)/2
If we replace x and y with jt and kt, we have
sin jt + sin kt = 2 cos t(j-k)/2 sin t(j+k)/2
If j and k are very close, (j-k)/2 would be nearly zero, so the cos term
would be nearly unity. Then we would have just
sin jt + sin kt = 2 sin t(j+k)/2
In other words, a sine wave who's frequency is the arithmetic mean of
the frequences of the two waves being added. QED.
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