I want to, and do, hire people who are smarter than I am. But I don't hire obnoxious fatheads.
-- John Larkin Highland Technology, Inc jlarkin at highlandtechnology dot com http://www.highlandtechnology.com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom laser drivers and controllers Photonics and fiberoptic TTL data links VME thermocouple, LVDT, synchro acquisition and simulation
And it's an entirely sensible unit for measuring FM, or Doppler shift from an accelerating body, or....
(I'm in the middle of an expert witness gig in which a lot is riding on the distinction between power and power spectral density. Units matter!)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net
Good luck. Maybe 1% of the population (and 0.1% of journalists) know that a KW is different from a KWH.
-- John Larkin Highland Technology, Inc jlarkin at highlandtechnology dot com http://www.highlandtechnology.com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom laser drivers and controllers Photonics and fiberoptic TTL data links VME thermocouple, LVDT, synchro acquisition and simulation
Think trigometry.
cos (A + B) = cos A . cos B - sin A .sin B
cos (A - B) = cos A . cos B + sin A . in B
Whence sin(A).sin(B)= 0.5 . Cos(A-B) - 0.5 Cos(A+B)
The product of a 30Hz sine wave and a 60Hz sine wave (as generated by sticking them into the X and Y inputs of a four-quadrant multiplier) is the sum of a 30Hz cosine wave and 90Hz cosine wave - which is to say a pair of phase shifted sine waves.
Your 18kHz represents a rather comic misapprehension.
-- Bill Sloman, Nijmegen
***************************Wow! I learn something new here all the time. The OP asked for A*B. (Regardless whether A*B makes any sense.) Now I learn that A*B = sin(A)*sin(B) Furthermore the cos(A)*cos(B) term can be ignored to make one's point. Where do I sign up to be a AGW zealot? I understand the rules now. Art
essage
ve
KHz.
as a
aOn the other hand you haven't fired yourself, so your judgement is clearly less than reliable.
-- Bill Sloman, Nijmegen
r!)
You clearly spend time with the wrong 1% of the population. But beggars can't be choosers.
-- Bill Sloman, Nijmegen
Hmm...
I don't know if there is no mathematical way to do this in the analog state how ever, using some FFT's (DFT) and (IDFT)'s One could then use math at a software level to regenerate a signal based from two values.
Jamie
Stay tuned, you don't understand, yet!
Slow-Man is here to save the planet! I have no idea what I'd do with out his guidance!
Jamie
No, it is not 18 kHz, as many have pointed out.
When it is said that it is a "multiplier," it means multiplication in the time domain. (And thus convolution in the frequency domain.)
It is basic trig, and it has been given by others already. Pick the form you want.
It is easy in software. Just do array multiplication, quite literally. cos(w1*t)*cos(w2*t). You have to decide your w1, w2, and t vector. Use python or whatever you want.
Or, you can use an identity form such as 0.5*cos((w1+w2)*t)
+0.5*cos((w1-w2)*t).Actually, doing these types of multiplications in software is how I have double checked some special trig identity formulations I computed.
For "eternal sinusoids," the frequency domain convolution is easier if you just want to know frequency and amplitude.
-- A wise choice, since two in a company would no doubt be counter-productive.
Incorrect. A multiplier is a linear device, with respect to a single input. For a function: f(A, B) = A * B it is true that (B != 0, and not a function of x or y): f(c1*x + c2*y, B) = B*(c1*x + c2*y) which is the definition of linearity.
Since the function has two inputs, it is more exactly bilinear, which is not linear with two dependent inputs, but it is most certainly not non-linear in general.
Tim
-- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms
-- Mathematically pure - whatever that's supposed to mean - or not, what I described will work.
"Tim Williams"
** I did not post the above.Da Slow Man did.
Watch what you are doing
"John Larkin"
** You gotta admit that some code scribbling wanker taking the term " frequency multiplier " absolutely literally IS pretty damn funny.Betcha the same fool thinks that a bottle of " steak sauce " contains steak.
.... Phil
Thanks to everyone for the input to my naive OP. I can now see it is a far more complex matter than I had first imagined.
I simply wanted to know if there is an equivalent dynamic function to "summing" based upon multiplication instead of addition.
And what would be the result if viewed on a spectum analyzer.
If I generate 30Hz and 60Hz in the tone generator of an audio editing application, and then "mix" them, a complex wave is obtained comprised of the two frequencies.
If I mix them in hardware, a sum and difference (beat) frequency would be added.
I am not aware what type of process would result in multiplication, based upon either of these two approachs. Or what the multiplied product would look like.
Of course I can generate a 1.8KHz sinewave directly, but that is not a process of interaction.
Excuse me for still being dense, but I am in over my head and using a straw.
Klaus Jensen
In the audio mixing case, you get a spectrum with both signals, and the result is useful because people like to hear drums and vocals together.
In the radio mixing case (which is what you mean when you say "mix in hardware"), you can use the signal at the sum or the difference frequency to make a superheterodyne radio possible -- and you can implement a radio- style mixer in a number of different and useful ways.
But that's as far as it goes. There really isn't any common, useful process that gives you a "frequency A * frequency B" result -- if nothing else, when you subject your question to dimensional analysis you find that when you multiply 30Hz times 60Hz, you do _not_ get 1800Hz (even though I fell into that trap). You get 1800(Hz)^2. Or maybe you get
71061 radians^2/sec^2. Whatever you get, unless you divide it by a reference frequency you have an acceleration, not a rate.-- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
"Klaus Jensen"
** This Wiki describes what a "frequency multiplier" is:Your mad idea is undefined and therefore idiotic.
Piss off.
... Phil
If you want to generate 18000 Hz from 60 Hz, that is the 300th harmonic.
The tradititional way is to use two x2 one x3 and two x5 multiplier stages.
With such low (18 kHz) frequency, the simplest way would be using a VCO phase locked to the 60 Hz reference with a divide by 300 counter.
-- There is heterodyning, where two sinusoidal sources are multiplied and the resultant frequencies are the original frequencies plus their sum and difference.
Not very well. The "count the input frequencies" part will have ambiguity. If you use a 1-second timebase for the count operation, each of the counted values will have a 1 count uncertainty from measurement to measurement. The final output frequency will jump around several per cent. If you freeze the VCO voltage, it stops tracking the inputs and hangs at the last, ambiguous, frequency.
In other words, it's another asynchronous hairball.
The linear-multiplier operation, the one that makes the sum and product frequencies, is mathematically perfect, so can be electronically approximated very closely.
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.