Assignment 9

Wiener Filter

Used for signal estimation, very similar to Kalman Filter. We also filter out the unwanted signal, $W[n]$.

Optimal MSE Filtering

We want to minimize the MSE, and find this filter

$$h_{opt}[n]=\text{ce}argminE(D-Y{)}^2$$

Where D is the desired signal, and Y is what we measure.

Optimum MSE FIR Wiener Filter

Resources: 12.7.1

Noncausal IIR Wiener Filter

Resources: 12.7.4

$$H(f)=\frac{{\Gamma }_{DX}(f)}{{\Gamma }_{XX}(f)}=\frac{{\Gamma }_{DS}(f)}{{\Gamma }_{SS}(f)+{\Gamma }_{WW}(f)}$$Link to original

c)

d)

The rectangular window typically shows sharper cutoff but more pronounced sidelobes (ripples in the stopband).

The Hamming window has a smoother transition band and reduced sidelobes, offering better overall frequency response characteristics in many applications.

e) Using this instead Gives us this response Which is exactly the same as before

Problem 2

b)

Problem 3