Hi I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized?
Sum of sine waves with min peak value
Started by ●February 27, 2013
Reply by ●February 27, 20132013-02-27
On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote:> Hi > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized?do you have to get close or an exact answer?
Reply by ●February 28, 20132013-02-28
On 2/27/2013 8:35 PM, Jim craig wrote:> Hi > > I would like to add together a group of about 10 sine-waves that are > all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume > all the amplitudes are equal. How can I set the phases of each > component such that the peak value is minimized?The key word is "Newman phase". See this paper: http://www.stanford.edu/~boyd/papers/pdf/multitone_low_crest.pdf Vladimir Vassilevsky DSP and Mixed Signal Designs www.abvolt.com
Reply by ●February 28, 20132013-02-28
On Feb 27, 10:57�pm, brent <buleg...@columbus.rr.com> wrote:> On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > Hi > > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized? > > do you have to get close or an exact answer?If I had to do this I would probably go about it by setting the first frequency to 0 phase, then add in the second and decide what phase minimizes F1+F2. I would then add in F3 to this and figure out which phase minimizes the F3 + (F1+F2) combination. I would keep adding in one more and optimizing its phase while keeping the phase settings of the previous ones the same. This would be my first attempt at an empirical method.
Reply by ●February 28, 20132013-02-28
On Wednesday, February 27, 2013 10:57:09 PM UTC-5, brent wrote:> On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > Hi > > > > > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized? > > > > do you have to get close or an exact answer?Close is fine
Reply by ●February 28, 20132013-02-28
On Wednesday, February 27, 2013 11:02:18 PM UTC-5, Vladimir Vassilevsky wrote:> On 2/27/2013 8:35 PM, Jim craig wrote: > > > Hi > > > > > > I would like to add together a group of about 10 sine-waves that are > > > all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume > > > all the amplitudes are equal. How can I set the phases of each > > > component such that the peak value is minimized? > > > > The key word is "Newman phase". > > See this paper: > > http://www.stanford.edu/~boyd/papers/pdf/multitone_low_crest.pdf > > > > Vladimir Vassilevsky > > DSP and Mixed Signal Designs > > www.abvolt.comThanks, looks interesting, I'll give it a read.
Reply by ●February 28, 20132013-02-28
On Feb 27, 11:05�pm, Jim craig <jimcraig...@gmail.com> wrote:> On Wednesday, February 27, 2013 10:57:09 PM UTC-5, brent wrote: > > On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > > Hi > > > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized? > > > do you have to get close or an exact answer? > > Close is fineIf close is fine, set up a program which randomizes all the phases and gives the peak answer. Run the program several hundred times and see what kind of spread you get and see if a bottom is looking like it is emerging. If a bottom seems to be emerging from the random data, then pick the set which is closest to the bottom.
Reply by ●February 28, 20132013-02-28
On Wednesday, February 27, 2013 11:24:31 PM UTC-5, brent wrote:> On Feb 27, 11:05�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > On Wednesday, February 27, 2013 10:57:09 PM UTC-5, brent wrote: > > > > On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > > > > > > Hi > > > > > > > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized? > > > > > > > do you have to get close or an exact answer? > > > > > > Close is fine > > > > If close is fine, set up a program which randomizes all the phases and > > gives the peak answer. Run the program several hundred times and see > > what kind of spread you get and see if a bottom is looking like it is > > emerging. If a bottom seems to be emerging from the random data, then > > pick the set which is closest to the bottom.The paper that Vlad mentioned suggests that quadratic phase gives an optimal result. It's interesting that when you add a large number of sine waves using quadratic phase, the sum resembles a frequency chirp. Somehow this seems like the right answer.
Reply by ●February 28, 20132013-02-28
On 2/27/13 11:06 PM, Jim craig wrote:> On Wednesday, February 27, 2013 11:02:18 PM UTC-5, Vladimir Vassilevsky wrote: >> On 2/27/2013 8:35 PM, Jim craig wrote: >> >>> Hi >> >>> >> >>> I would like to add together a group of about 10 sine-waves that are >> >>> all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume >> >>> all the amplitudes are equal. How can I set the phases of each >> >>> component such that the peak value is minimized? >> >> >> >> The key word is "Newman phase". >> >> See this paper: >> >> http://www.stanford.edu/~boyd/papers/pdf/multitone_low_crest.pdf >> >> >> >> Vladimir Vassilevsky >> >> DSP and Mixed Signal Designs >> >> www.abvolt.com > > Thanks, looks interesting, I'll give it a read.this is kinda weird, but long long ago (1999) i was helping review submissions for the IEEE WASPAA (a.k.a. Mohonk) and one of the papers whas this http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=810884 from Ivo Mateljan. it's about this multisine, low crest thing. i reviewed it, it was accepted, and then when the conference happened (which was not too far from my NJ home), the author was a no show. couldn't make it over from Croatia. anyway, the day before when his paper was scheduled, they asked me as a reviewer to present what i thought was the kernel and i agreed to. since he presented it as an alternative to Maximum Length Sequences (because of known problems with MLS), i mostly talked about what i knew was good (lowest possible crest and "white" in a cyclical sense) and also what's wrong with MLS (those spurious spikes in the apparent impulse response due to non-linearities). about his method, all's i can remember it was a multisine thing with phases initially set to random. but he had some thing where you would mess with some particular sinusoid that was sorta most responsible for whatever peak that was determinative of the crest factor. i have a .pdf of the reviewed copy on an old computer (with Mac OS 9) that i haven't fired up for a while, and then i have the proceedings (and maybe a CD from the convference) somewhere, but i still have lotsa stuff in boxes. i'll try to look it up somewhere. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●February 28, 20132013-02-28
On Thursday, February 28, 2013 4:57:09 PM UTC+13, brent wrote:> On Feb 27, 9:35�pm, Jim craig <jimcraig...@gmail.com> wrote: > > > Hi > > > > > > I would like to add together a group of about 10 sine-waves that are all harmonically related (for example, 10Hz, 20Hz ... 100Hz). Assume all the amplitudes are equal. How can I set the phases of each component such that the peak value is minimized? > > > > do you have to get close or an exact answer?try the maths for two first!
