Write a C$++$ program to

$1)$ read the real$-$valued data from the input text file called filexx $($where xx is a number$).$

$2)$ apply the following filter to the data

filtered$\_$output$(0)=$ unfiltered$\_$input$(0)$

filtered$\_$output$($n$)=0\mathrm{.}9375*$ filtered$\_$output$($n$-1)+0\mathrm{.}0625*$ unfiltered$\_$input$($n$)$

$3)$ print the original data and the filtered data into the output file called outputfilexx $($where xx is a number$).$ The following format should be used

HH$.$H TT$.$TTTTTT

where

HH$.$H represents original data

TT$.$TTTTTT represents the filtered data with $6$ decimal digits of precision.

Each entry should be separate by a single tab character $(\backslash$t$).$

For example, if the original data is

$67\mathrm{.}7$

$67\mathrm{.}6$

$67\mathrm{.}7$

$67\mathrm{.}6$

$67\mathrm{.}6$

$67\mathrm{.}3$

$67\mathrm{.}4$

the output is

$67\mathrm{.}767\mathrm{.}700000$

$67\mathrm{.}667\mathrm{.}693750$

$67\mathrm{.}767\mathrm{.}694141$

$67\mathrm{.}667\mathrm{.}688257$

$67\mathrm{.}667\mathrm{.}682741$

$67\mathrm{.}367\mathrm{.}658819$

$67\mathrm{.}467\mathrm{.}642643$

Observations:

$1)$ the first data $($at index $0)$ has no filter

$2)$ the second data on the second column $67\mathrm{.}693750$ is from

$0\mathrm{.}9375*$ filtered$\_$output$($n$-1)+0\mathrm{.}0625*$ unfiltered$\_$input$($n$)=0\mathrm{.}9375*67\mathrm{.}7+0\mathrm{.}0625*67\mathrm{.}6$

$3)$ the third data on the second column $67\mathrm{.}694141$ is from

$0\mathrm{.}9375*$ filtered$\_$output$($n$-1)+0\mathrm{.}0625*$ unfiltered$\_$input$($n$)=0\mathrm{.}9375*67\mathrm{.}693750+0\mathrm{.}0625*67\mathrm{.}7$