0.3 Reconstruction using Linear Interpolation

To reconstruct the signal, using the Shannon-Whittaker interpolation formula, we need an ideal lowpass filter. Let us see other interpolation methods, like linear interpolation$\bar{y}$. This is built into the plot function in matplotlib.

Linear interpolation of the samples obtained from the bandlimited signal.

The reconstruction is not accurate, but it fairly approximates the bandlimited signal. We also see that the linearly interpolated signal and the bandlimited signal, both, are consistent with the samples -- which brings us back to the fact that sampling is inherently ill-posed. There is more than one way to recover a continuous-time signal from discrete samples.

Checkpoint:

• Can linearly interpolated signals be bandlimited signals?

• What type of signals can be sampled and perfectly reconstructed by linear interpolation?

• Can you think of a generalisation to Shannon's sampling framework that includes linearly interpolated signals?