# Signal reconstruction given non-impulse sampling

With sampling modeled as a multiplication with a dirac comb, we can recover the original signal perfectly with a low pass filter given that the sample-rate criterion is satisfied.

What about a more practical case where the signal is sampled with a pulse train, and not an impulse train? E.g. rectangular pulse train with varying duty cycle (99.999% duty cycle could represent an ideal CCD pixel array). Is there a way to recover the original signal perfectly? Any pointing directions to reading about this matter would be appreciated, the only term I could find is "aperture error" but it does not point to the generalized theoretical case. Thanks

• You mean that the actual sampled signal is something like $x_n = \int_{n T_s - T_w}^{n T_s} x(\tau) d\tau$, where $T_s$ is the sampling interval and $T_w$ is an integration window? Dec 9, 2022 at 22:35

When the signal is sampled with a pulse train, we multiply in time the signal with the pulse which is the same as convolving in frequency the Fourier Transform of the signal with the Fourier Transform of the pulse. The Fourier Transform of a pulse of width $$T$$ seconds is a Sinc with the first null in frequency at $$1/T$$ Hz. This convolution in frequency will "smear" the spectrum, and will be inconsequential if the width of the pulse is significantly less than the bandwidth of the signal.