**Question 12**

The Inverse Discrete Fourier Transform of the sampled frequency response was taken to obtain the impulse response h(n).

The resulting response was graphed:

**Stem Graph**

**XY Plot**

The impulse response matches the results obtained in question 5, as expected.

The Matlab Code from 12 can be seen here.

**Optional Part**

The question was repeated using Matlab and the standard FFT routine using N = 1024.

The graph of the impulse response obtained matches with the manually calculated results:

The frequency resolution was found to be .

The Matlab Code from 12(Optional) can be seen here.