magnitude response of IdQ-QdI
in [DSP]
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From: jacobfenton on 24 May 2010 15:44 I am trying to find the mathmatical magnitude response of the following FM demodulation equation: I[n-1]*(Q[n]-Q[n-2])-Q[n-1]*(I[n]-I[n-2]) ----------------------------------------- I[n-1]^2+Q[n-1]^2 How do I represent I and Q in terms of some x[n] to find the z transform of the equation? I know I[n]=x[n]*cos(phi) and Q[n]=x[n]*-sin(phi). But phi is also a function of 'n'. Not sure what to do here. Thanks. -Jacob Fenton
From: Steve Pope on 24 May 2010 15:58 jacobfenton <jacob.fenton(a)n_o_s_p_a_m.gmail.com> wrote: >I am trying to find the mathmatical magnitude response of the following FM >demodulation equation: > >I[n-1]*(Q[n]-Q[n-2])-Q[n-1]*(I[n]-I[n-2]) >----------------------------------------- > I[n-1]^2+Q[n-1]^2 >How do I represent I and Q in terms of some x[n] to find the z transform of >the equation? >I know I[n]=x[n]*cos(phi) and Q[n]=x[n]*-sin(phi). >But phi is also a function of 'n'. Not sure what to do here. There is not enough information here. If you know the statistics of phi(n), you can then compute the correlations between pairs of signals such as Q[n] and Q[n-2], I[n] and Q[n], and you can then come up with an analytic form for the magnitude of the above ratio. (Or if you happen to know all these signals are uncorrelated then the answer is simple, but they are almost certainly not.) Steve
From: Vladimir Vassilevsky on 24 May 2010 16:11 jacobfenton wrote: > I am trying to find the mathmatical magnitude response of the following FM > demodulation equation: > > I[n-1]*(Q[n]-Q[n-2])-Q[n-1]*(I[n]-I[n-2]) > ----------------------------------------- > I[n-1]^2+Q[n-1]^2 ~ 2WT School math. > Not sure what to do here. Break your stupid head against the wall.
From: Clay on 25 May 2010 10:11 On May 24, 3:44 pm, "jacobfenton" <jacob.fenton(a)n_o_s_p_a_m.gmail.com> wrote: > I am trying to find the mathmatical magnitude response of the following FM > demodulation equation: > > I[n-1]*(Q[n]-Q[n-2])-Q[n-1]*(I[n]-I[n-2]) > ----------------------------------------- > I[n-1]^2+Q[n-1]^2 > > How do I represent I and Q in terms of some x[n] to find the z transform of > the equation? > I know I[n]=x[n]*cos(phi) and Q[n]=x[n]*-sin(phi). > But phi is also a function of 'n'. Not sure what to do here. > > Thanks. > > -Jacob Fenton First let's assume your analytic signal is truly analytic, then feed a sinusoid into the system and see what you get: Thus I(n) is A*cos(2*pi*n*f/fs) and Q(n)=A*sin(2*pi*n*f/fs) plug it in and reduce (you only need a few trigonometric identities), and you will get sin(2*pi*f/fs) for your result fs is the sample rate, f is the frequency and A is the arbitrary amplitude. IHTH, Clay
From: Clay on 25 May 2010 10:19
On May 25, 10:11 am, Clay <c...(a)claysturner.com> wrote: > On May 24, 3:44 pm, "jacobfenton" <jacob.fenton(a)n_o_s_p_a_m.gmail.com> > wrote: > > > I am trying to find the mathmatical magnitude response of the following FM > > demodulation equation: > > > I[n-1]*(Q[n]-Q[n-2])-Q[n-1]*(I[n]-I[n-2]) > > ----------------------------------------- > > I[n-1]^2+Q[n-1]^2 > > > How do I represent I and Q in terms of some x[n] to find the z transform of > > the equation? > > I know I[n]=x[n]*cos(phi) and Q[n]=x[n]*-sin(phi). > > But phi is also a function of 'n'. Not sure what to do here. > > > Thanks. > > > -Jacob Fenton > > First let's assume your analytic signal is truly analytic, then feed a > sinusoid into the system and see what you get: > > Thus I(n) is A*cos(2*pi*n*f/fs) and Q(n)=A*sin(2*pi*n*f/fs) > > plug it in and reduce (you only need a few trigonometric identities), > and you will get > > sin(2*pi*f/fs) for your result > > fs is the sample rate, f is the frequency and A is the arbitrary > amplitude. > > IHTH, > Clay I left out a factor of two, the result is 2*sin(2*pi*f/fs) Clay |