Problem 1. Sampling & Quantization (10 points) In this problem, we intend to study the effects of sampling and quantization on digital images Your job is to write a function with the following specifications (you may use loops if necessary): (i) The function takes one input: the image file name. (ii) The input image is assumed to be in grayscale. (iii) Sample the image in spatial domain with a sampling rate of 8 (your image should be approx- imately 8 times smaller along width and height, do not use any MATLAB functions) (iv) Do a5-level uniform quantization of the sampled image so that the bins cover the whole range (v) Repeat the quantization as in previous step but do it with 3-level quantization this time. Note (vi) The function returns three output: the sampled image; the sampled and 5-level quantized of grayscale values (0 to 255). You should not use any MATLAB functions for this. that this 3-level quantization is done on the sampled image before the 5-level quantization image; and the sampled and 3-level quantized image. Evaluate your function on the image image1.png and save all the returned images to be included in the report. Things to turn in: The original image; the image after sampling; the image after both sampling and 3-level quantization; and the image after both sampling and 5-level quantization. Response for the following questions How would the above function be of use in image compression? Based on the resulting images, what can you say about how sampling an