$1.$ A causal first$-$order infinite impulse response $($IIR$)$ low$-$pass filter is described by the following difference equation: $15$ points$)$ y$[$n$]+0\mathrm{.}8$y$[$n$-1]-$x$[$n$],$ a$)$ Determine its frequency response. b$)$ Find the magnitude and phase responses c$)$ Find the impulse response of the filter d$)$ Determine the maximum value of the magnitude response.