[LAD] Determining Phase

Duncan Gray duncang at catraeus.com
Mon Jun 27 00:50:18 UTC 2011

On the subject of the word Quadrature:

The word Quadrature is shorthand for the imaginary component of a 
complex-valued variable. Furthermore, it is almost exclusively used in 
the domain of carrier modulated waveforms. The word for the real 
component is In-Phase. That is why so many texts on the subject use I 
and Q to describe these two concepts. This choice of words was due to 
the fact that some radiomen in the '20s created a 90-degree delayed 
signal from the carrier (a quatrature relationship with respect to the 
carrier in the ancient college trigonometry literature) and (I doubt 
ignorantly) left out the fact that it was simply a practical way to 
perform complex analysis on a narrow-band waveform.

It was unfortunate that you used the mathematically reserved word 
complex to describe a complicated signal. The concept of quadrature in 
an audio baseband signal assumes a single frequency, say 1000 Hz., 
wherein that arbitrarily chosen "carrier" is assumed for Quadrature 
analysis. In fact, the Fourier Transform assumes an infinite number of 
such carriers to create a continuous, complex-valued transform of the 
pure real audio channel. The FFT is a Discrete Fourier Transform that 
periodizes the waveform to create a finite number of discrete carriers, 
each at the bin related to the length of the transform. Each bin of 
frequency output by that transform has a real and an imaginary component 
-- Quadrature.

@Gordon, please remember that your SDAR code ASSUMES the carrier 
frequency so as to be able to analyze Quadrature. It is a more 
complicated concept in general complex analysis of a broadband signal 
such as audio.

-- In the limit as productivity approaches infinity all jobs become 
entertainment or neurosis.

On 06/26/2011 05:02 PM, Gordon JC Pearce wrote:
> On Sun, 26 Jun 2011 14:54:48 -0400
> gene heskett<gheskett at wdtv.com>  wrote:
>> I do not see how a repeatable, and therefore measurable quadrature
>> component can be developed in a complex, multi-frequency waveform since the
>> quadrature component is just as frequency dependent as any other method of
>> measurement.
> Really?  Because I'm generating some quadrature samples right now - they're how software-defined radios work.  In this case you generate two local oscillators 90 degrees apart and use them to switch a pair of synchronous detectors.  The resulting downmixed RF is now at audio frequencies (just like a direct-conversion receiver) and can be passed to a soundcard, then processed on the PC to extract a particular signal.
> See https://github.com/gordonjcp/lysdr if you want to play.
> Gordon MM0YEQ
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