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Let $Y_{n}=s_{n}+W_{n}$ where $\left\{s_{n}\right\}$ is the desired signal bandlimited to $[-W, W]$ and $\left\{W_{n}\right\}$ is a noise component, which is sparse (that is, only few samples are non-zero), bursty (that is, runs of non-zero samples are rare), and its amplitude is large compared to the desired signal. Which of the following filtering techniques is preferable?

  1. Low pass filter with cutoff at $\text{W}$
  2. High pass filter with cutoff at $W$ is used first (to estimate $W_{n}$ ) and the output of the high pass filter is subtracted from the input
  3. Bandpass filter with suitable cutoffs
  4. The output at time $n$ is chosen to be the median of $\left\{Y_{n+k}\right\}_{k=-K}^{K}$ for suitably chosen $K$
  5. Both $a)$ and $b)$ are better than the other options
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