# 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.](https://1719691385-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MetmKF4Nky-_P8tzlc8%2F-Mih7X3shsACh9VlVXJX%2F-Mih7sW4u_vFgttpHwol%2Fimage.png?alt=media\&token=e4f8fd35-bb2b-4fb0-8d78-ec8ca4ad8a31)

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.

{% hint style="success" %}
**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?
  {% endhint %}
