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1

To downsample an FFT result for both magnitude and phase, it may work best to do an FFTShift before the FFT, then downsample the real component vector and then the imaginary component vector separately, before taking the atan2() of them to estimate downsampled phase.


4

A real-valued system that doesn't distort the shape of the input signal must have the following input-output relation: $$y(t)=Ax(t-t_0)\tag{1}$$ with arbitrary real-valued constants $A>0$ and $t_0$. In the frequency domain, Eq. $(1)$ corresponds to $$Y(\omega)=Ae^{-j\omega t_0}X(\omega)\tag{2}$$ Consequently, the corresponding system is an LTI system ...


1

For a phase distortion metric I recommend using “group delay variation”. The definition of Group Delay is the negative derivative of phase with respect to frequency. The Group Delay is the delay in time that “group” of signals over a band of frequencies would have. A frequency response that is linear in phase (constant group delay with no variation) is not ...


0

A lot of radar systems are interested in measuring Doppler, one example of which is pulse Doppler (PD) radar. PD radars are capable of measuring both range and velocity (with ambiguities, but that’s a different topic). The basic idea behind a PD radar is to transmit many pulses of the same waveform and observe how the phase of a target return changes. To ...


0

Yes. Simply sum all the polyphase outputs and the sum result will have higher resolution. Consider that each polyphase output is a delayed version of the same signal, so that if you commutated through all the outputs, you would get a higher sampled version of your same signal and the quantization noise of this signal would be approximately white across this ...


1

This is an untested time domain solution, but the math looks solid. This will be impossible to implement unless you solve the reciever synchronization problem first. That is either a hardware fix or a calibration operation. Assume it is solved and your two signals are coming in as time aligned sequences. Assume also your sampling rates (I don't like "...


0

If your signal is at least somewhat oversampled, you could try the following time domain approach; 1) Apply the output of each A/D to a Hilbert Transform filter to generate a complex signal. 2) Derive the sample-by-sample angle for each complex signal by using ATAN2. 3) Designate 1 channel as the reference channel. For every reference clock and subsequent ...


0

Is there any single shot solution for comparing the relative phase difference between the signals received with different sampling frequencies as mentioned? Yes it is, as long as you have an exact knowledge of the timing relationship between the samples for each receiver. It's complicated, but if you understand the properties of the Fourier transform it's ...


0

I would not rule out hardware effects. The input stage of the AC measurement path in a DMM will include a variable-gain amplifier to auto-range the input so that the ADC noise and non-linearity are minimized. It's possible that the bandwidth (and therefore phase) is not constant as a function of gain (although it sounded as if you are inputting a pretty low ...


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