Optimal Wiener Filtration

Filtering sound signals using Wiener Filter

The signal for this project can be found on the web page in EE. It is in the file ”boli.sig”.
Consider only the first 512 values of the signal. Case N = 512.
1. Process this signal f(n) degraded by the following smooth filter
h = [• • • , 0, 1, 2, 3, 3, 2, 1, 1, • • •]/13, (h(0) = 3)
i.e., calculate the circular convolution g(n) = f(n) * h(n), where n = 0 : (N − 1).

Convolution can be done in frequency domain
Inverse filters are commonly used in signal restoration. The common application for Inverse filters is signal deblurring; in such applications the signal is blurred with a filter and then noise is added. The main task of Inverse Filter is to restore the original signal given the characteristics of the blurring operation.
The most common approach to Inverse filter is to do the inverse operation of blurring (do deblurring).
The inverse filter can perform better with the absence of noise. However, transmission media is not ideal. Noise must be considered in any filter design. Wiener Filter objective is to de-blur the signal with noise added. The idea is to consider the Signal to Noise Ratio. When the noise is approximately zero, the resulting filter will be exactly an Inverse Filter, when there is noise; Wiener Filter will be adaptively adjusting the signal according to the Signal to Noise Ratio