Re: [LAD] Determining Phase

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. @Gene: 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. Duncan -- In the limit as productivity approaches infinity all jobs become entertainment or neurosis. On 06/26/2011 05:02 PM, Gordon JC Pearce wrote: