I have a set of sensors, some velocity-meters and others accelerometers. To process the two groups together, I integrate the accelerometers signals (in time domain, using MATLAB's cumsum
), so I'll have all sensor data now in velocity. Knowing the precise arrival time of a signal at different sensors are very important in determining the location of the signal source. Wondering if I am introducing some phase shift by integration, I tried to estimate the group delay. I am not sure what I am doing is right though. Given that the integrator can be written as:
$$y(n) = x(n) + y(n-1)$$
the filter coefficients will be
\begin{align} a&=\begin{bmatrix}1 &-1\end{bmatrix}\\ b&=\begin{bmatrix}1 & 0\end{bmatrix} \end{align}
Giving these values to the MATLAB's grpdelay
function (Group delay), I get a constant value across all frequencies of half a sample.
- Does it mean that my signal after integration is shifted by half a sample regardless of frequency ?
- And what about zero frequency (the mean value), why is the group delay 0.5 sample at 0?