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# CmpE 362: Homework 3: Frequency Domain Filtering and Processing solved

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## 1 Introduction

In this homework, you will implement some simple frequency domain exercises with MATLAB.

In this part, you will improve your peak detection algorithm that you developed in the first homework.
You will design a low pass lter (See Chapter 6 : Frequency Response of FIR Filters for detailed description)
For this lter, you will change the limit frequency of the low pass filter between 1000Hz, 2000Hz, 3000Hz
and 4000Hz. You will apply these four different low pass filters with cut off frequencies (1k,2k,3k,4k) and
plot number of peaks versus changing cut off frequencies. (Add no filter also). Add these plots to your pdf

## 1.2 Converting a Hubble Deep Space Image Into Space Sound

In this part, you will convert a Hubble deep space image into space sound. The image is provided in
HW3materials.zip file as Hubble Massive Panorama. You will examine the image as columns. Starting
with the first column you will examine each pixel whether it is black or not. There are 900 pixels in each
column. If a pixel in the column is not black, it means there is a celestial body in the pixel. Divide 900
pixel in the column into 10 parts.

Starting from the bottom of the picture, index parts in decreasing order
from 10 to 1. If a non-black pixel exists in any part, create an amplitude in the nth pixel frequency with
index of the part amplitude. As an example, if there is a non-black exist in 68th pixel of a column, you will
create 10 amplitude in 68Hz. If a pixel is black, create a zero amplitude in the corresponding frequency.
By applying these rules, you will have different amplitudes from 0 to 900 Hz.

After you create 1024 spectra that have different amplitudes from 0-900Hz, convert each of them into
time domain. Duration of each spectrum must be 1 second. Concatenate each one-second wav files one after
another and create a wav signal that has length of 1024 seconds. Name your script as SonifiedDeepSpace.m.
In the last line of your MATLAB script, play the created sound. (Hint: You can use Fourier Transform
and Inverse Fourier Transform when converting between time and frequency domains. )

## 1.3 Report and Notes

Prepare a report explains your code briefly. Add the figures and codes to the pdf report. Explain your code
with comments. Compress the report and the code files. Name it as ”YourNumber CmpE362 HW3.zip”.
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