Re: Gap in beat freqs.
- From: Martin Brown <|||newspam|||@nezumi.demon.co.uk>
- Date: Fri, 14 Mar 2008 11:45:47 +0000
In message <7oqjt3hor85v6im5ko33fqk6l3jlhbqhgh@xxxxxxx>, Bob Steiner <bobsteiner@xxxxxxxxxxxx> writes
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?
If you assume linear mixing at equal amplitude and pure sine waves then you can use the trig identity to work out what the equivalent multiplicative description would be.
Sin(X) + Sin(Y) = 2 Sin((X+Y)/2).Cos((X-Y)/2)
You don't actually create any real new frequencies by linear mixing. Whereas combining in a multiplier will generate new frequencies.
For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.
So 10MHz + 9MHz equal mixed is equivalent to 9.5MHz carrier frequency with a multiplicative envelope modulation of 0.5MHz.
And 1.00001 MHz + 10Hz equally mixed is equivalent to having
0.50001MHz multiplied by 0.5MHz.
In this case the nearly 1MHz wobbling up and down on a slowly changing baseline is probably the more intuitive description to work with.
PS: I am not referring to stability of the oscillator.
When the two frequencies are close together in one of the descriptions they are far apart in the other.
Regards,
--
Martin Brown
--
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