(Solved): The transfer function for this filter is given by Figure 1: Location of two zeros for simple a FIR ...

The transfer function for this filter is given by Figure 1: Location of two zeros for simple a FIR filter $$H_f(z)=\left(1?z_1{z}^{?1}\right)\left(1?z_2{z}^{?1}\right)=\left(1?e^{j?}{z}^{?1}\right)\left(1?e^{?j?}{z}^{?1}\right)=1?2\cos ?z^{?1}+z^{?2}$$ Task 6 (10 marks): Use this transfer function to determine the difference equation for this filter. Then draw the corresponding system diagram and compute the filter's impulse response $$h(n)$$. This filter is an FIR filter because it has an impulse response $$h(n)$$ of finite length. Any filter with only zeros and no poles (other than those at 0 and $$\pm ?$$ ) is an FIR filter. Zeros in the transfer function represent frequencies that are not passed through the filter. This can be useful for removing unwanted frequencies in a signal. The fact that $$H_f(z)$$ has zeros at $$e^{\pm j?}$$ implies that $$H_f\left(e^{\pm j?}\right)=0$$. This means that the filter will not pass pure sine waves at a frequency of $$?=?$$ Use Matlab to compute and plot the magnitude of the filter's frequency response $$\left|H_f\left(e^{\pm j?}\right)\right|=0$$ on $$???<?$$ for the following three values of $$?$$ : $$?=?/6;?=?/3;?=?/2$$ Put all three plots on the same figure using the subplot command. Consider this issue: 1. How the value of $$?$$ affects the magnitude of the filter's frequency response. In the next experiment, we will use the filter $$H_f(z)$$ to remove an undesirable sinusoidal interference from a speech signal.