Suppose two 16 bit words define the frequency of two sine waves from 0.1Hz to 20 Khz +/-0.1Hz which are then summed, amplified by "infinity" and then clipped, giving a pulsed output. In theory, I think this could be done using a DSP to do everything, but what's the best strategy? Method 1: 1. Store a Nyquist sampled sinewave in Eprom 2. upsample the lower frequency to that of the higher frequency and add together 3. MMmm... this is getting tricky OK. Is there an algorithm that gives us the times for which a sampled waveform crosses zero and whether the gradient is positve or negative? If so, then EURIKA!! since this defines when the pulse should go positive or negative. Method 2: 1. Use a mathematical expression for sin(2*pi*f*t) to calculate the sum at intervals of 1/(10*f) where f is the larger of the two and then iterate further to find the zero crossing point and gradient. I suspect there is a closed form mathematical expression that defines the zero crossing points and the derivatives. Again, probably slow in calculating but the easiest to understand. Funky
convert sum of two sines to square wave?
Started by ●February 16, 2004
Reply by ●February 16, 20042004-02-16
"Funky" <hello@hello.com> wrote in message news:c0re09$ifl$1@newsg1.svr.pol.co.uk...> Suppose two 16 bit words define the frequency of two sine waves from 0.1Hz > to 20 Khz +/-0.1Hz which are then summed, amplified by "infinity" and then > clipped, giving a pulsed output. In theory, I think this could be doneusing> a DSP to do everything, but what's the best strategy? > > Method 1: > 1. Store a Nyquist sampled sinewave in Eprom > 2. upsample the lower frequency to that of the higher frequency and add > together > 3. MMmm... this is getting tricky > > OK. Is there an algorithm that gives us the times for which a sampled > waveform crosses zero and whether the gradient is positve or negative? > If so, then EURIKA!! since this defines when the pulse should go positiveor> negative. > > Method 2: > 1. Use a mathematical expression for sin(2*pi*f*t) to calculate the sum at > intervals of 1/(10*f) where f is the larger of the two and then iterate > further to find the zero crossing point and gradient. >> I suspect there is a closed form mathematical expression that defines the > zero crossing points and the derivatives. Again, probably slow in > calculating but the easiest to understand.Sin (2*pi*(f1+f2)*t) + Sin (2*pi*(f1-f2)*t) = 2*Sin (2*pi*(f1)*t)Cos (2*pi*(f2)*t) So the Zeros of the RHS are easily calculated, as is the derivative which is just Cos (2*pi*(f1+f2)*t) + Cos (2*pi*(f1-f2)*t) evaluated at these points. Clever, eh?;)> Funky > > > >
Reply by ●February 16, 20042004-02-16
Funky wrote:> Suppose two 16 bit words define the frequency of two sine waves from 0.1Hz > to 20 Khz +/-0.1Hz which are then summed, amplified by "infinity" and then > clipped, giving a pulsed output. In theory, I think this could be done using > a DSP to do everything, but what's the best strategy? > > Method 1: > 1. Store a Nyquist sampled sinewave in Eprom > 2. upsample the lower frequency to that of the higher frequency and add > together > 3. MMmm... this is getting tricky > > OK. Is there an algorithm that gives us the times for which a sampled > waveform crosses zero and whether the gradient is positve or negative? > If so, then EURIKA!! since this defines when the pulse should go positive or > negative. > > Method 2: > 1. Use a mathematical expression for sin(2*pi*f*t) to calculate the sum at > intervals of 1/(10*f) where f is the larger of the two and then iterate > further to find the zero crossing point and gradient. > > I suspect there is a closed form mathematical expression that defines the > zero crossing points and the derivatives. Again, probably slow in > calculating but the easiest to understand. > > FunkyIt seems to me that the straightforward way is to fun two standard sinusoidal oscillators, sum them, and then set the output to 1 or -1 according to whether the sign of the result is positive or negative. Is there a reason not to do that? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 16, 20042004-02-16
Funky wrote: ...> Sin (2*pi*(f1+f2)*t) + Sin (2*pi*(f1-f2)*t) = 2*Sin (2*pi*(f1)*t)Cos > (2*pi*(f2)*t) > > So the Zeros of the RHS are easily calculated, as is the derivative which is > just Cos (2*pi*(f1+f2)*t) + Cos (2*pi*(f1-f2)*t) evaluated at these points. > > Clever, eh?;)What's the gain? You still have the sum of two sinusoidal oscillators. Your expression becomes more complex if you want to give the two basic sines different amplitudes. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 16, 20042004-02-16
Maybe I don't understand the problem, by why use trig functions (expensive) at all if you just want to generate square waves? That's an easy integer-only operation and computationally cheap. Am I missing something? Brian "Jerry Avins" <jya@ieee.org> wrote in message news:40314fc1$0$3090$61fed72c@news.rcn.com...> Funky wrote: > > > Suppose two 16 bit words define the frequency of two sine waves from0.1Hz> > to 20 Khz +/-0.1Hz which are then summed, amplified by "infinity" andthen> > clipped, giving a pulsed output. In theory, I think this could be doneusing> > a DSP to do everything, but what's the best strategy? > > > > Method 1: > > 1. Store a Nyquist sampled sinewave in Eprom > > 2. upsample the lower frequency to that of the higher frequency and add > > together > > 3. MMmm... this is getting tricky > > > > OK. Is there an algorithm that gives us the times for which a sampled > > waveform crosses zero and whether the gradient is positve or negative? > > If so, then EURIKA!! since this defines when the pulse should gopositive or> > negative. > > > > Method 2: > > 1. Use a mathematical expression for sin(2*pi*f*t) to calculate the sumat> > intervals of 1/(10*f) where f is the larger of the two and then iterate > > further to find the zero crossing point and gradient. > > > > I suspect there is a closed form mathematical expression that definesthe> > zero crossing points and the derivatives. Again, probably slow in > > calculating but the easiest to understand. > > > > Funky > > It seems to me that the straightforward way is to fun two standard > sinusoidal oscillators, sum them, and then set the output to 1 or -1 > according to whether the sign of the result is positive or negative. > Is there a reason not to do that? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > ����������������������������������������������������������������������� >
Reply by ●February 17, 20042004-02-17
Brian Reinhold wrote:> Maybe I don't understand the problem, by why use trig functions (expensive) > at all if you just want to generate square waves? That's an easy > integer-only operation and computationally cheap. Am I missing something? >Yes, I think it's trivial. You only need to know the periods (and initial phases) of the two sine waves and then you have all the information you need. You need to take care of the fractional component of the period with sufficient resolution, but that's not /too/ hard. No need for any trig. Paul
Reply by ●February 17, 20042004-02-17
Paul Russell wrote:> Brian Reinhold wrote: > >> Maybe I don't understand the problem, by why use trig functions >> (expensive) >> at all if you just want to generate square waves? That's an easy >> integer-only operation and computationally cheap. Am I missing >> something? >> > > Yes, I think it's trivial. You only need to know the periods (and > initial phases) of the two sine waves and then you have all the > information you need. You need to take care of the fractional component > of the period with sufficient resolution, but that's not /too/ hard. No > need for any trig. > > PaulThe assumption again seems to be that the amplitudes of the two sine waves are equal. Is that confirmed? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20042004-02-17
"Jerry Avins" <jya@ieee.org> wrote in message news:40326df7$0$3094$61fed72c@news.rcn.com...> Paul Russell wrote: > > > Brian Reinhold wrote: > > > >> Maybe I don't understand the problem, by why use trig functions > >> (expensive) > >> at all if you just want to generate square waves? That's an easy > >> integer-only operation and computationally cheap. Am I missing > >> something? > >> > > > > Yes, I think it's trivial. You only need to know the periods (and > > initial phases) of the two sine waves and then you have all the > > information you need. You need to take care of the fractional component > > of the period with sufficient resolution, but that's not /too/ hard. No > > need for any trig. > > > > Paul > > The assumption again seems to be that the amplitudes of the two sine > waves are equal. Is that confirmed?Yes, the amplitudes are equal.> Jerry > -- > Engineering is the art of making what you want from things you can get. > ����������������������������������������������������������������������� >
Reply by ●February 17, 20042004-02-17
Funky wrote:> > Yes. I still think you need to exploit the trig identity that sum of sines > equals product of sin and cos, unless you're thinking of another way.I don't think so. Given the intial phases and the periods all you need is a simple state machine. (As others have noted, it gets more complicated if the amplitudes of the two sine waves are different, but apparently that is not the case in this instance.) Paul
Reply by ●February 17, 20042004-02-17
"Paul Russell" <prussell@sonic.net> wrote in message news:PztYb.1835$_3.30431@typhoon.sonic.net...> Brian Reinhold wrote: > > > Maybe I don't understand the problem, by why use trig functions(expensive)> > at all if you just want to generate square waves? That's an easy > > integer-only operation and computationally cheap. Am I missingsomething?> > > > Yes, I think it's trivial. You only need to know the periods (and > initial phases) of the two sine waves and then you have all the > information you need. You need to take care of the fractional component > of the period with sufficient resolution, but that's not /too/ hard. No > need for any trig.Yes. I still think you need to exploit the trig identity that sum of sines equals product of sin and cos, unless you're thinking of another way. Funky> Paul > >
