Re: [Discuss-gnuradio] White Noise detection and elimination

[Robert James]

On 11/18/13, Marcus Müller <address@hidden> wrote:
> Hi Robert,
>
> Your explanation of "going from complex to real" did not make much sense
> to me, sorry. You can't go from complex to real, the former vector space
> is a superset of the latter, and thus there is no reversible mapping
> from complex to real.
>
> Hope that helps a little bit :)
> Greetings,
> Marcus
>
> On 18.11.2013 18:25, Robert James wrote:
>> Got it: The Fourier coefficients tell you *two* things per freq:
>> amplitude and phase.  In real values (what I'm used to), those are two
>> distinct numbers.  In complex values (welcome to DSP), it's one
>> complex number, telling you the amplitude of the 0-degree component
>> (Re) and the amplitude of the -90-degree component (Img).
>>
>> Going from complex to real is easy: complex r  = real amplitude,
>> complex theta = real phase.  But that's besides the point.  The point
>> is that amplitude alone is only half the story, phase is the other
>> half, and, without phase, you can't reconstruct the original signal.
>> (The FFT displays might not show the phase, and we might not alwasy
>> talk about it, but it's half the information, like it or not.)

Thanks Marcus.  By "going from complex to real" I simply mean that
given complex Fourier coefficients, we can easily map that to real
amplitude (abs(z)) and real phase (angle(z)).  In other words, a
vector of complex Fourier coefficients is the same thing as 2 real
valued vectors, one for amplitude, one for phase - just in a different
form.  Is that not correct?