Consider an impulse response $h[n]$ such that $h[n]=0$ for $n<mn\; id="EditorElement\_2119939">0</mn>$ and $n>M,$ and $h[n]=$

$-h[M-n]$ for $0nM$ where $M$ is an odd integer.

a$)$ Express the Fourier transform of $h[n]$ in the form

$H(e^j)=e^{jf()}A(),$

where $f()$ and $A()$ are real$-$valued functions of $.$ Determine $f()$ and $A().$

b$)$ Provide an example of such an impulse response $h[n]$ for $M=7$ and find the corresponding

$f()$ and $A().$