### Task 1

More Symbolic Algebra

%Lab 7 Task 1 close all; clear; clc; syms x y; %y=x^2+5*x+6; figure fplot('x^2+5*x+6',[-50 50]) figure ezpolar('cos(x)') figure ezpolar('2+cos(x)') figure ezpolar('sin(x)+cos(x)') figure ezplot('cos(x)')

### Task 2

Laplace Transform and Inverse Laplace Transform

%Lab 7 Task 2 close all; clear; clc; syms t a s; y=exp(-a*t); pretty(laplace(y)) y1=exp(3*t); pretty(laplace(y1)) pretty(laplace(heaviside(t))) y2=exp(3*t)+exp(-5*t); pretty(laplace(y2)) fs=(7*s-6)/(s^2-s-6); pretty(ilaplace(fs))

### Task 3

FFT in MATLAB

%Lab 7 Task 3 %Fourier Transform using FFT close all; clear; clc; f=100; fs=10*f; t=0:1/fs:1; y=cos(2*pi*f*t); figure plot(t,y) %NFFT = 2^nextpow2(length(t)); NFFT=1024; z=fft(y,NFFT); z=z(1:length(t)/2 +1); freq=0:length(t)/2; freq=freq*fs/NFFT; figure plot(freq,abs(z))

%Lab 7 Task 3_1 %Fourier Transform using FFT for a different function close all; clear; clc; f=100; fs=10*f; t=0:1/fs:1; y=cos(2*pi*f*t)+sin(2*2*pi*f*t); figure plot(t,y) %NFFT = 2^nextpow2(length(t)); NFFT=1024; z=fft(y,NFFT); z=z(1:length(t)/2 +1); freq=0:length(t)/2; freq=freq*fs/NFFT; figure plot(freq,abs(z))