Re: Is this correct?

[Sergei Steshenko]

----- Original Message -----
> From: Macy <address@hidden>
> To: address@hidden
> Cc: 
> Sent: Friday, April 25, 2014 8:11 PM
> Subject: Is this correct?
> 
>T his is a problem 'interpretting' a swept tone in octave.
> The fft plot looks like it's too wide a spectrum.
> 
> Not sure why, or what is going on here.
> The idea was to sweep from 300MHz to 400MHz: and doing so I expected ONLY 
> energy 
> in that spectral range, after all it is a slow sweep. 
> 
> fixed tone as a reference:
> fc=300e6;dt=1/10/fc;N=120000;
> t=[0:1:N-1]*dt;
> sig=sin(2*pi()*fc*t);
> b=fft(sig)/N;
> produces a plot with appropriate spike(s)
> 
> ok now I wish to sweep the tone from 300MHz up to 400MHz
> sig=sin(2*pi()*1e6*(300+100*([0:N-1])/N).*t);
> which should make a tone sweep from 300MHz up to 400MHz, right?
> when I plotted the fft, it looked like the energy went from 300MHz up to 
> 500MHz 
> ??!!
> 
> so went back and plotted
> plot(t(1:100),sig(1:100));
> hold on;
> plot(t(1:100),sig(end-100+1:end))
> hold off;
> is ok, time range held the same just for 'marking'
> 
> The frequency did indeed look like 300MHz at the low end and high at the end, 
> like almost 400MHz
> If go from 400MHz down to 300MHz: 
> sig=sin(2*pi()*1e6*(400-100*([0:N-1])/N).*t);
> then the fft appears to go from 400MHz down to 200MHz ??!!
> 
> What I'm missing is why this is NOT equivalent. the start determines an 
> EXACT edge and the ending frequency becomes twice its frequency. What?
> 
> The implication to me is that there is energy in those bands, else the fft 
> would 
> NOT show it. This is boggling my mind. The implication is that a low pass 
> filter 
> will act differently upon a low to high vs a high to low chirp. Perhaps the 
> sweep was not as slow as I thought. something else to check. I'll check both 
> premises soon, but right now I'm having difficulty wrapping my head about 
> these results. 
> 
> Are they correct? Is this right?
> 
> 
> 
> 
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Frequency modulation has infinitely wide spectrum.

E.g. http://en.wikipedia.org/wiki/Frequency_modulation :
"
While most of the energy of the signal is contained within fc ± fΔ, it can be 
shown by Fourier analysis that a wider range of frequencies is required to 
precisely represent an FM signal. The frequency spectrum of an actual FM signal 
has components extending infinitely, although their amplitude decreases and 
higher-order components are often neglected in practical design problems.[4]
".

Regards,
  Sergei.