Question

Frequency Shaping Filters There are many applications of frequency shaping filters including audio systems in which systems permit listeners to modify the relative amounts of low-frequency energy (bass) and high- frequency energy (treble). Also, frequency shaping filter can be used to smooth the data. We will implement an LTI system that can take two-point average of the input values: y[n] = (x[n] + x[n – 11) In this case h[n] = {(8[n] +8[n – 1) The frequency response of the system is: Heim) = {(1+e-jº) = e =ju/cos (w/2) Write a MATLAB script to apply the filter on the data provided on Moodle and show the following six plots using subplot. Original signal x[n] in time domain Signal X(w) in frequency domain Filter h[n] in time domain Filter H(w) in frequency domain Output signal y[n] in time domain Output Yiw) in frequency domain Modify the above example by implementing an LTI system that can take four-point average of the input values. Write h[n] and Hiw) expressions for the filter.

Data File from excel

Date	Open	High	Low	Close	Adj Close	Volume
2019-02-25	111.76	112.18	111.26	111.59	110.1329	23750600
2019-02-26	111.26	113.24	111.17	112.36	110.8928	21536700
2019-02-27	111.69	112.36	110.88	112.17	110.7053	21487100
2019-02-28	112.04	112.88	111.73	112.03	110.5671	29083900
2019-03-01	112.89	113.02	111.67	112.53	111.0606	23501200
2019-03-04	113.02	113.25	110.8	112.26	110.7941	26608000
2019-03-05	112.25	112.39	111.23	111.7	110.2414	19538300
2019-03-06	111.87	112.66	111.43	111.75	110.2908	17687000
2019-03-07	111.4	111.55	109.87	110.39	108.9485	25339000
2019-03-08	109.16	110.71	108.8	110.51	109.067	22818400
2019-03-11	110.99	112.95	110.98	112.83	111.3567	26491600
2019-03-12	112.82	113.99	112.65	113.62	112.1364	26132700
2019-03-13	114.13	115	113.78	114.5	113.0049	35513800
2019-03-14	114.54	115.2	114.33	114.59	113.0937	30763400
2019-03-15	115.34	117.25	114.59	115.91	114.3965	54681100

Answer 1

MATLAB code is given below in bold letters.

clc;
clear all;
close all;

% load the data
load moddle.txt;

% read the data
Open = moddle(:,1);
High   = moddle(:,2);
Low   = moddle(:,3);
Close   = moddle(:,4);
Adj_Close = moddle(:,5);
Volume = moddle(:,6);

% % define the filter 2 point
% b2 = [1/2 1/2];a2=1;

% define the filter 4 point
b4 = [1/4 1/4 1/4 1/4];a4=1;

% obtain the filtered outputs
open_filtered = filter(b4,a4,Open);
High_filtered = filter(b4,a4,High);
Low_filtered = filter(b4,a4,Low);
Close_filtered = filter(b4,a4,Close);
Adj_Close_filtered = filter(b4,a4,Adj_Close);
Volume_filtered = filter(b4,a4,Volume);

% plot the original and filtered
figure;
subplot(231);
plot(1:length(Open),Open,1:length(open_filtered),open_filtered);
legend('original','4-point filter');title('Open');

subplot(232);
plot(1:length(High),High,1:length(High_filtered),High_filtered);
legend('original','4-point filter');title('High');

subplot(233);
plot(1:length(Low),Low,1:length(Low_filtered),Low_filtered);
legend('original','4-point filter');title('Low');

subplot(234);
plot(1:length(Close),Close,1:length(Close_filtered),Close_filtered);
legend('original','4-point filter');title('Close');

subplot(235);
plot(1:length(Adj_Close),Adj_Close,1:length(Adj_Close_filtered),Adj_Close_filtered);
legend('original','4-point filter');title('Adj_Close');

subplot(236);
plot(1:length(Volume),Volume,1:length(Volume_filtered),Volume_filtered);
legend('original','4-point filter');title('Volume');

Open High Low -original – 4-point filter original 4-point filter original 4-point filter 108 106 100 2 4 6 8 10 12 14 10 15 2 4 6 8 10 12 14 Close Adjclose Volume 6* 107 original 4-point filter original 4-point filter - original - 4-point filter 2 4 6 8 10 12 14