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Do you need a DFT for a sinusoid?
No need for a full DFT. So it is very efficient as well. By placing the frequency squarely near the center of the two bins you minimize noise effects and avoid needing to deal with near bin frequencies which call for a different set of equations for the fitting vector. The alternative form is for when the frequency is really close to a bin.
How many bins to find phase between sinusoids?
Phases in the second half will be negative. You can’t do better than this for accuracy in my experience. Select a frame size of 1 1/2 cycles or 2 1/2 cycles. You only need to calculate two bins, either 1 and 2, or 2 and 3.
How is FFT related to phase distortion in ARG?
Notice third and fifth harmonics in an ABS (FFT) graph and nearly full circle phase noise in ARG (FFT): which generates FFT like in the below picture It would be interesting to know the origin of those github datasets and how they are related with phase noise/phase distortion.
But the current’s FFT shows a nonlinearity of voltage-to-current conversion (if the dataset’s current is generated from the dataset’s voltage by some electronic circuit). Notice third and fifth harmonics in an ABS (FFT) graph and nearly full circle phase noise in ARG (FFT):
Can a frequency demodulator be a complex sinusoid?
Frequency demodulators are similarly trivial: just differentiate the phase of the complex sinusoid to obtain its instantaneous frequency.
How is a complex sinusoid related to a phase quadrature?
Thus, a complex sinusoid consists of an “in-phase” component for its real part, and a “phase-quadrature” component for its imaginary part. Since , we have. That is, the complex sinusoid has a constant modulus (i.e., a constant complex magnitude).
How to write a formula for sinusoidal frequency modulation?
A general formula for frequency modulation of one sinusoid by another can be written as where the parameters describe the carrier sinusoid, while the parameters specify the modulator sinusoid. Note that, strictly speaking, it is not the frequency of the carrier that is modulated sinusoidally, but rather the instantaneous phase of the carrier.