acceleration resampling

[FengqiuAdamDong]

Hello,
I am looking at the resample_tim function and I can not work out where the formulation comes from.
This is clearly different from the pulsar handbook and Camillo et al 2000

##THIS CODE IS COPIED FROM SIGPYPROC3, https://github.com/FRBs/sigpyproc3/blob/main/sigpyproc/core/kernels.py
@njit("f4[:](f4[:], f4, f4)", cache=True, parallel=True)
def resample_tim(array: np.ndarray, accel: float, tsamp: float) -> np.ndarray:
    nsamps = len(array) - 1 if accel > 0 else len(array)
    resampled = np.zeros(nsamps, dtype=array.dtype)

    partial_calc = (accel * tsamp) / (2 * CONST_C_VAL)
    tot_drift = partial_calc * (nsamps // 2) ** 2
    last_bin = 0
    for ii in prange(nsamps):
        index = int(ii + partial_calc * (ii - nsamps // 2) ** 2 - tot_drift)
        resampled[index] = array[ii]
        if index - last_bin > 1:
            resampled[index - 1] = array[ii]
        last_bin = index
    return resampled

The version in the handbook and Camollo et al 2000 gives the formulation

In saying that, it seems to work. I have used it successfully to de-modulate the orbit of binaries in Ter 5

[pravirkr]

Hi,

Apologies for the late response.

This is the same formulation as in the paper, just implemented as a computationally fast approximation.

The code assumes $\tau_{0} \approx t_{samp}$(which is true when aT/2c << 1). So, we are not transforming time intervals, but simply calculating a time shift for each sample. The delay equation is
$$t_{corrected} = t_{obs} - a \cdot (t_{obs} - t_{mid})^2 / 2c$$
In sample indices, this is
$$ii_{new} = ii + (a \cdot t_{samp} / 2c) \cdot (ii - n_{samps} / 2)^2 - t_{offset}$$

The $t_{offset}$ (or tot_drift) is subtracted to pin the endpoints to re-center the transformation.

If you have an alternative formulation or want to add a new exact method, feel free to open a PR.