Linear mixing of two generated frequencies is the electronic equivalent of mathematical "addition". This can be easily demonstrated in function generator software.
What then is the software equivalent of "multiplying" two sinewave frequencies together?
For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz. And what does the resulting signal look like?
I am aware of "multiplier" IC's, but want to do this in software as a purely mathematical function.
Klaus Jensen
Think trigometry.
cos (A + B) =3D cos A . cos B - sin A .sin B
cos (A - B) =3D cos A . cos B + sin A . in B
Whence sin(A).sin(B)=3D 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
"Klaus Jensen"
** Oh no it don't. ** Then go find out what they ACTUALLY do.... Phil
First, it helps to know what 2 times 3 is..better brush up on your math. Second, it helps what the term "multiplying" means in this context. Then you might have a chance..
"Klaus Jensen"
** In electronics, "linear mixing" is normally just called "summing".Egs: summing amplifier, summing stage etc
The idea of "linear mixing" likely comes from the world of recording and live sound.
Egs: mixing desk, mixing engineer, the mix etc
Every sound mixing desk contains numerous summing amplifiers which take inputs from each channel and sum them.
.... Phil
"Bill Slowman"
** Wanna put the code scribbling newb out of his misery by defining what a " frequency multiplier " actually is ?Tip: think whole numbers ...
... Phil
If you mathematically multiply two sine waves (or use an analog multiplier) you get the sum and difference frequencies, as Sloman points out in his usual obnoxious way.
There's no simple or even fundamental way to multiply two frequencies. The result would depend on your units of measure.
In Hz, 30 * 60 = 1800
but if you think of those same sine waves in radians,
(30 * 2 * pi) * (60 * 2 * pi) = 71057
which is not the same thing.
-- John Larkin Highland Technology Inc www.highlandtechnology.com jlarkin at highlandtechnology dot com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators
a "
A frequency multiplier is a non-linear device - such as a four quadrant multiplier - that exploits the trignometric relationships that I pointed out generate sum frequencies. The newb's 30Hz multiplied by 60Hz to get 90Hz is a trivial case.
If you want high multiples of the driving frequency, you use a part that converts a sine wave into an approximation to series of Dirac spikes, whose Fourier transform contains equal amplitudes of every harmonic of the fundamental up to a limit set by the width of the spike.
Since the Dirac spike has zero width by definition, it transforms into an infinite number of harmonics, each with a with vanishingly small amplitude.
Step recovery diodes generate edges with fall times down to about
100psec - which is to say, harmonics up to 10GHz. They are real and useful.-- Bill Sloman, Nijmegen
What's obnoxious about spelling out the fundamental trignometrical basis of what's going on? Does it bruise you sensitive ego by reminding you of the classes you skipped because you were too busy to see their relevance?
Give John another life-time or two and he'll discover dimensional analysis.
-- Bill Sloman, Nijmegen
"Bill Slowman"
A frequency multiplier is a non-linear device - such as a four quadrant multiplier - that exploits the trignometric relationships that I pointed out generate sum frequencies. The newb's 30Hz multiplied by 60Hz to get 90Hz is a trivial case.
** Oh dear, I thought I was handing Bill a piece of cake.But he turned it into a big, brown, smelly turd.
Making EXACTLY the same "comic" mistake as the f****it code scribbler.
... Phil
Calling a basic misunderstanding a "comic misapprehension."
-- John Larkin Highland Technology Inc www.highlandtechnology.com jlarkin at highlandtechnology dot com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators
He blames his unemployment on age. I bet the HR people are just doing a Usenet search and finding what an asshole he is.
--- Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
18kHz.If that's what you really want, then in very general terms, what I'd do would be to count the input frequencies, store the values to two registers, say "x" and "y", then multiply the contents of the registers and store the result in "z".
Next, I'd ramp up a VCO, count its output frequency, and compare that to the contents of "z".
When they're equal I'd clamp the voltage driving the VCO's frequency, and at that point the VCO's output frequency would be equal to the product of the two AC input signals.
-- JF
I wouldn't hire him at half his age. I suspect not many others would, either.
-- John Larkin Highland Technology Inc www.highlandtechnology.com jlarkin at highlandtechnology dot com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators
You are confused. I'm not even sure what you're basing that statement on, but in RF design (which is I assume where you're pulling your terms), a "frequency mixer" multiplies two signals together, at least one of which is a sine wave or a distortion thereof, resulting in a signal that has a spectrum with energy at the sum and difference frequencies of the frequency content in the two original signals.
Nonsense.
Well, as John Fields pointed out, multiplying 30Hz by 60Hz results in
1800Hz, so you're arithmetic is wrong. The resulting signal looks like whatever you want it to, because there isn't any widely-used useful signal processing function that does this.A "frequency multiplier" and a "multiplier" are two different things. A "frequency multiplier" takes a sine-wave signal and runs it through some nonlinearity to generate a repetitive wave at the sine-wave frequency, then filters out one of the resulting harmonics -- so you can start with frequency f, and get 2f, 3f, etc. A plain old "multiplier" just multiplies two voltages: V_out = (V_1 * V_2)/(V_ref), where V_ref is some reference voltage that's either explicit, or (more usually) inherent in the design of the multiplier circuit.
Back up a few steps and tell us -- at a system level -- what you are trying to _do_. Not "I want to multiply two frequencies together", but tell us what you're building, what it needs to do, and why you need to do this oddball thing to succeed.
-- 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
There is no mathematically pure way to do this. It depends on an artifact, namely the second. If you measure the frequencies in KHz, or MHz, or radians, you get a wildly different answer.
-- John Larkin Highland Technology Inc www.highlandtechnology.com jlarkin at highlandtechnology dot com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators
age
. aCheck out Parkinson's Law on injelititus.
It starts when some up-himself prick refuses to hire people who might be smarter than he is ...
-- Bill Sloman, Nijmegen
ge
aDon't be silly. HR people aren't clever enough to do anything like that.
-- Bill Sloman, Nijmegen
Actually, 1.8kHz^2. Metre^2 is a meaningful unit. because we live in a three dimensional universe. Einstein demonstrated that we actually live in a four dimensional universe, where time is an imaginary number. If it was five dimensional, with two mutually orthogonal imaginary time axes, Hz^2 might be a meaningful unit, but my imagination isn't up to envisaging how.
Isn't dimensional analysis fun.
-- Bill Sloman, Nijmegen
Well, it's actually 1800 (Hz^2), or 1800 / (sec ^ 2). It's an acceleration, not a rate.
-- Dave Platt AE6EO Friends of Jade Warrior home page:
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