"Scott Gardner" wrote in message

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that
"varies the amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency, phase and amplitude. In fact, just slightly more than two
samples is sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.

It's a theorem that has never been disproved that says that it takes
slightly more than 2 points to adequately define a unique sine wave.

I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes at
zero seconds, 1 second, and 2 seconds are all zero, I've given you
three different points along the wave.

Right, but the frequency of that wave has to be outside the range for which
the theorem applies.

From this, the period can be
measured and the frequency derived from that, but I don't see how I've
given you enough information to calculate the amplitude.
Let me know what I'm missing.

You are missing the fact that the frequency of a signal with three points
that are zero is too high for the Nyquist theorem to apply. In fact, the
frequency of the signal has to be exactly half the sample rate.

Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

At least one of the points has to be non-zero, and this will be true if the
frequency of the signal is even just slightly below half the sample rate. At
exactly half the sample rate, the signal can have any amplitude and have
three zero samples. It's a well-known boundary condition.