I have read somethiong like the following process is possible, but am unsure how to implement it. Any suggestions would be appreciated.

Say you have a mix of 10 sinewaves from 100Hz t0 500 Hz, random with no harmonic relationship to each other.

Let's say one of these frequencies is 400Hz. Is there an 11th frequency that can be added to the mix that will, due to some mathematical property, suppress the amplitude of the 400Hz?

I have no further details on how this is supposed to work, other than it might involve a log relationship to 400Hz.

The idea suggests that the transient voltage at certain points iin the waveform can be counteracted with the result of a net loss in signal level.

And that this technique relies upon applying a different frequency, not simply a phase inverted 400Hz.

No -- sine waves of different frequencies (and also of 90 degree phase shifts) are orthogonal.

Consider the integral int(f(t) * g(-t) dt) for sine waves:

infty / | e^(j*a*t) * e^(-j*b*t) dt /

-infty

When a != b, the functions (the exponentials) have different frequencies and the integral evaluates to nonzero. If a = b, the exponents subtract and cancel, resulting in a zero integral. (Actually, that gets int(e^0 dt), which evaluates to t. I'm sure I forgot something fundamental. At any rate, it's a different result from the case when a != b, where the integrand is the difference phase shifted.)

It also follows that, if you can somehow select and recover the 400Hz signal (typically, filtering with a narrow bandpass, or tracking with a PLL), you can subtract it (nulling by amplitude and phase shift) and completely remove that signal, without affecting the rest of the signal. (The inverse of a bandpass filter is a notch filter, so if you took the former approach, you wouldn't filter and subtract, you'd use a notch in the first place.)

Yes, it does make sense... and the answer is "yes and no".

If the "mix" of sinewave signals is purely a linear additive one, then the answer is going to be "no". That is, if you have ten sinusoidal signals

S1 = A1 cos (F1 * T + D1) S2 = A2 cos (F2 * T + D2) S3 = A3 cos (F3 * T + D3)

...

S = S1 + S2 + S3 + ... + S10

and one of these signals is at 400 Hz, and none of the others are... then there is (mathmatically and practically) no way to eliminate the 400 Hz signal other than cut it off at the beginning (set the amplitude An to zero), or inject another signal which has exactly the same frequency and is 180 degrees out of phase. The other signals are at different frequencies and, no matter how many of them there are, the fact that they're being combined in a purely linear fashion (by adding) means that there's no way to take any two of these cosine functions and get something which will be at 400 Hz and will result in a cancellation of the unwanted signal.

Now, if the initial sinewaves are being "mixed" by a nonlinear process, then *every* pair of the input frequencies will create at least two "sidebands" or "mixing products": these will occur at the sum, and difference of the two frequencies. For example, if S1 happened to be at 500 Hz and S2 at 600 Hz, the result of mixing them in a nonlinear fashion will product a signal containing some 100 Hz and some 1100 Hz component (difference and sum).

So, in this situation, you would in theory be able to add an 11th frequency which was 400 Hz above or below one of the other frequencies, and creating a mixing product at 400 Hz. Set the amplitudes and phases of the various input signals right and you could perhaps create a 400 Hz component which was out of phase with the unwanted 400 Hz signal and would null it out.

I doubt that it's a practical solution, though. For one thing, the incoming 400 Hz signal is going to mix with all of the other signals to create a whole bunch of sideband mixing products, and you will probably *not* be able to null those out in the same way. Adding the

11th "cancellation" signal is going to create even *more* sidebands.

Hence, you probably won't be able to get rid of the 400 HZ signal "cleanly" through this sort of cancellation process.

no you cannot reduce the amplitude of___the 400 Hz___ but you can find another signal to add to the mix that may reduce the PEAK amplitude _____ of the total____ of all the signals.

If you are considering time window of a finite length, then yes, this is possible. You just have to do decompose 400 Hz into Fourier basis of other frequencies.

On a sunny day (Sat, 19 Oct 2013 06:00:59 -0500) it happened "Dave M" wrote in :

Yes, that is a possible way to operate. And if the '400 Hz' is for example 'hum' with its own harmonics, then you can use an comb filter that also attenuates all the harmonics of the 400 Hz. (Or 50 Hz, or 60 Hz more likely). It does not make the audio any better, but can be a saver of bad material:

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And if the source is a wave file you can run as many test as you want to get it right.

Google ISCO Proteus or dANF filter. They do it with RF using advanced DSP.

I realize that's not even close to your posted inquiry, but it's still pretty amazing what they can do along the lines of removing narrowband interference from a huge swath of spectrum.

Yes, and that is only one of the things that really burns me up. As someone else here stated days ago, if you agree to pay the workers, they should work for it just like the rest of us. They closed facilities so that the public would be aggravated and, in a sense, held the citizens of the US hostages. This entire episode should be considered a crime against the public.

I have lost all faith in our so-called "government for and by the people". I will not vote for any incumbent in the upcoming elections.

You bet there is. The National Guard here didn't get paid, evidently. It's in the state constitution that state employees don't get back pay for furloughs.

Good grief! If the 17% of government employees who were on furlough for TWO WEEKS were owed $328B, well, it would explain a lot! Hell, if the entire cost of government for that two weeks were $328B, it would explain a lot. That would be, um, $8.53T per *YEAR*, NEGLECTING the taxes received during that time. Things are bad, really bad, but not

*that* bad. No, the explanation is simpler than that. The administration broke the law (wow! That's a first!).

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