Re: 24-bit on tap at Apple?

I suspect that for most LP lovers, this is the unique attraction.

Are you saying that it's not possible? Here, take my shovel, dig up Mr. Fourier, tell him it's not possible.

Take ANY amplitude-modulated waveform. Take it's Fourier transform. The result is some collection of continuous sine waves, n'est ce pas?

Let's look at a simple case: a 1 kHz wave modulated by a 100 Hz envelope. That's three sine components, whose relative amplitudes are dependent upon the amount of modulation: one sitting at 900 Hz, one at 1000 Hz, and one at 1100 Hz. Y'know, sidebands, and all that?

Take a more complex waveform with a more complex envelope, and it's merely an extension of the same thing.

That's right, that's what he was asking about.

Right - the needed memory jog - an amplitude modulated carrier has a certain spectrum. It picks up sidebands that are related to the modulating frequency.

Yup.

Yup.

I asked a question, you answered it. I'm embarassed to say that I once knew the answer but the fog of other battles, and all that.

Thank you.

You can simulate modulation by adding other signals (the sidebands) by means of linear mixing.

The over all process is nonlinear because new frequencies are added. But, the process that Dick described fit within my question about linear mixing. I didn't say that new frequencies couldn't be added.

You're both right as long as you don't say that Dick is wrong, per my question. ;-)

A quick handwaving version of how you do it is to choose a suitable mixture of sinewaves centred around the fundamental and its harmonics with the phases tweaked to have a sharp attack and a slow decay around the peak envelope position and to cancel elsewhere. It would not be an efficient representation of a piece of music but it could be done.

A more detailed explanation is that a multiplication of the signal in the time domain is a convolution in the frequency domain (and vice versa). That is amplitude modulation of a simple continuous carrier wave with or without harmonics can be achieved in the frequency domain by convolving with the Fourier transform of the envelope shape you want to impose. Shannons sampling theorem for a band limited function and the fact that the Fourier transform preserves all information allows a formal proof.

ISTR in the late 70's there was an infamous near unplayable direct mastered vinyl record of the 1812 which featured on the cover an electron micrograph of the offending groove. It destroyed expensive styluses as well as playing through very few times before failing.

Whilst you can produce an unplayable CD with laser readback it never damages the playback device though it might damage the speakers.

Regards, Martin Brown

I have always had the impression that you needed something similar of a continuous waveform to get the FFT, trying to take the FFT of a single pulse does not make a lot sense.

While the decaying part of the piano waveform could be simulated with a series of sine waves multiplied with a curve simulating the inversely exponentially dying out string oscillations, the attack part of the waveform is far more complicated.

You are both right and wrong. You are wrong in that the FFT couldn't care less what shape the waveform is. Provided its frequency is contained within half the sampling rate, it will reproduce it.

You are right - and this is where most people forget what an FFT really does - in that there is an implicit assumption within the FFT that the entire sample is repeated ad infinitum. In fact when you perform an FFT, you effectively join the ends together to make a loop.

It makes perfect sense. A single unit pulse gives essentially a continuous spectrum up to the first null occuring at, essential

No, just a wider bandwidth in its spectrum

NO I didn't. Someone asked about how continuous sine waves can have an envelope, someone else described it as "amplitude modulate" and I simply described one case as an example where an amplitude-modulated waveform can be decomposed into component, continuous sine waves. I never attempted or intended to describe how the process of modulation takes place, only how a collection of component sine waves can lead to that result.

The important point is that one can create an amplitude modulated (enveloped) signal by simple linear mixing of the right signals, or one can use that well-known nonlinear process called Amplitude Modulation. One also can also create a frequency modulated signal by simple linear mixing of a different and often far more complex collection of signals.

But does it work in a barber shop?

Kirk

Spewed tea all over my monitor.

Sherry in Vermont

At least it was tea, not beer...

Kirk

Wait. We don't?

Or spew ;-0

geoff