Recent content by sampsont

The DFT is defined as: Y(m) = ∑ x(n) e-jωnm/T I only care about m = 1 right now. Y(1) = ∑ x(n) e-jωn/T Y(1) = ∑ [x(n) cos(ωn/T) - x(n) jsin(ωn/T)] Dot product: U ⋅ V = ∑ U[n] V[n] It looks to me like the dot product is the first, (real) part of the DFT, where one of the vectors is an ideal...

Ahhh. The DFT coefficient of the fundamental frequency gives the phase between an ideal cosine with zero phase, and your signal. The linear algebra method does the same thing except the phase reference is your first vector instead of the ideal cosine. Is this correct?

Thanks, but what does θ really mean? My two vectors are each a cycle of the 60Hz from the power outlet. Each vector has 80 samples. What does the angle between my two vectors tell me? What can I use it for? Can it give me any indication of the relative phase of a sine waves?

The norm of a vector, in my case a sine wave is the RMS. There must be an integer number of cycles in the vector and you have to divide the norm by the number of samples. At least this much is intuitive. I'm still wondering what to make of the angle.

Thanks for the response! Much appreciated. Actually, I already have the phase and frequency measurements implemented using the DFT, and more specifically, the Goertzel algorithm which is an IIR filter that essentially achieves a single bin DFT. We have an A/D for each input channel so all...

The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I...