$1)$ HW$\_$resize$1$D $($float $*$IN$,$ float $*$OUT$,$int INlen, int OUTlen, int kernel$\_$type, double param$)$ Function HW$\_$resize$1$D scales the list of numbers stored in IN into a newlist OUT. IN has INlen elements of datatype float. OUT has OUTlen elements. If OUTLEN $>$ INLEN, then magnification must be performed. Else, minification takes place. In either case, the user specifies the filter through argument kernel$\_$type,which can be set to $0,1,2$ to refer to nearest neighbor, linear interpolation, and cubic convolution, respectively. Incubic convolution, the free variable a is passed through param. V alues $3,4,$ and $5$ for kernel$\_$type are reserved for windowed sinc functions. The corresponding windowfunctions that should be used are: Hann, Hamming, and Lanczos windows. Note that parameter N for the Hann and Hamming windows $($as used in the equations in the book$)$ are passed through param.That is$,$ param will store the width of the window. Inthe case of the Lanczos window, param is used to store the number of sinc lobes allowed to pass. For instance, the Lanczos$2($x$)$ windowwill be specified with param $=2,$ the Lanczos$3($x$)$ windowwith param $=3,$ etc. Test HW$\_$resize$1$D for magnification for a $1-$D impulse function. Initialize an array of $32$ numbers with $100$ everywhere, and $200$ at the center $($location $16).$ Then magnify this list by a scale factor of $8$ using all the above kernels. The output list of $256$ elements should match with the samples of the respective reconstruction kernels. Submit aplot of the output for each kernel. Remember to pad the input to avoid problems at the borders where the convolution kernel falls off the edge of the image. Use pixel replication for padding. Test HW$\_$resize$1$D for minification for a $1-$D sine wav e function having values lying between $0$ and $255.$ Initialize an array of $128$ numbers with a sine wav e having $16$ cycles per scanline $($or $\mathrm{.}125$ cycles per pixel$).$ Then minify this list by a scale factor of $8$ using all the above kernels. The output list will have $16$ elements. Submit aplot of the output for each kernel. Remember to pad the input to avoid problems at the borders where the convolution kernel falls off the edge of the image. Use pixel replication for padding. Also, note that unlikethe magnification case, minification will cause the kernel to be stretched wider and reduced in amplitude in proportion to the scale factor. $2)$ HW$\_$resize$2$D $($ImagePtr I$1,$ int new$\_$h$,$ int new$\_$w$,$int kernel$\_$type, int param, ImagePtr I$2)$ Function HW$\_$resize$2$D scales an image stored in I$1$and stores it in I$2.$ The dimensions of the output image is new$\_$h $($height; or rows$)$ by new$\_$w $($width; or columns$).$ This function implements scaling separably by first resampling each image scanline with calls to HW$\_$resize$1$D$,$putting the result into an intermediate buffer. Then, HW$\_$resize$1$D is invokedoneach column to yield the output image. Run this function on small images, such as eye$50.$pgm and text$40.$pgm$,$ to demonstrate magnification. Magnify by several scale factors, including $2,4,$ and $10.$ Over what scale factors are the various kernels acceptable?$-2$Describe the artifacts that appear, including their location and structure. Note that you will want to convert the unsigned char elements in I$1$tofloat for use in HW$\_$resize$1$D$,$and then convert back to unsigned char for storage in file I$2.$ Run HW$\_$resize$2$D on large images with a lot of high frequencies $($edges$),$ such as star.pgm$,$ to demonstrate minification. Compare the results between the point sampling $($nearest neighbor$)$ and a higher quality filter when minifying star.pgm or ramp.pgm$.$ Whydoes point sampling work well for the ramp.pgm image and not for star.pgm$?$