Use the MATLAB commands \(\mathrm{filt} \mathrm{ter}\), conv, and \(\mathrm{f} f \mathrm{t}\) to filter a given input signal, with the impulse response obtained in Exercise 12.9. Verify what must be done to the input signal in each case to force all output signals to be identical. Compare the processing time and the total number of floating-point operations used by each command, using tic, toc, and flops (see the MATLAB help for the correct usage of these commands).

Exercise 12.9.

Design a highpass filter using the minimax method satisfying the following specifications:

\[\begin{aligned}A_{\mathrm{p}} & =0.8 \mathrm{~dB} \\A_{\mathrm{r}} & =40 \mathrm{~dB} \\\Omega_{\mathrm{r}} & =5000 \mathrm{~Hz} \\\Omega_{\mathrm{p}} & =5200 \mathrm{~Hz} \\\Omega_{\mathrm{s}} & =12000 \mathrm{~Hz} .\end{aligned}\]

Determine the corresponding lattice coefficients for the resulting filter using the command you created in Exercise 12.3. Compare the results obtained using the standard command tf2latt.

Exercise 12.3.

Write down a MatLab command that determines the FIR lattice coefficients from the FIR direct-form coefficients.