matlab code:

% Lab 2: Signal generation

% How can we generate a discrete sigle using matlab

% For example if we have the signal's explicit formula

% we can generate its numeric approximation.

% And this example will show you that how we generate a

% signal y(t) with known support

% And y(t) = 3 ramp(t+3) - 6 ramp(t+1) + 3 ramp(t) - 3 unitstep(t-3)

% where ramp is continuous funciton = t u(t); its derivate is unit-step

% function

% while unistep function is a function with only 2 values in its domain.

% unitstep function u(t) equals to zero when t < 0 and u(t) = 1 when t >= 0

% therefore, in this system, we know that it is clear aformed by a time-invariant

% part unit-step and a time variant part ramp

clear all; clf;

% To plot numeric appromation, we need define the minimal step of each

% discrete point.

Ts = 0.01;

% Then, we plot the signal from -5 to 5; the support of it can be define as

% t

t = -5:Ts:5;

% Then, let us define the ramp signal function tu(t) and unit-step function

% in ustep.m and ramp.m. The we can write out the signal y as

y = ramp(t, 3, 3) + ramp(t, -6, 1) + ramp(t, 3, 0) - 3 * ustep(t, -3);

% result plot

figure(1)

plot(t, y, 'k');

axis([-5 5 -1 7]);

grid;

title('$$y(t)=3r(t+3)-6r(t+1)+3r(t)-3u(t-3)$$', 'interpreter', 'latex');

% Assignment 1.1

% plot this function, and please analysis each part of function y(t)

% For example, y(t) = 0 for t < -3 and t > 3, this imply us we selected

% t in [-5, 5] is proper.

% And then, please also write down the segment :

% -3 <= t <= -1

% -1 < t <= 0

% 0 < t <= 3

% section 2. When u study ECE 206/307. You will always use a very useful

% analysis on response signal summetry property.

% They are Even / Odd Signal of it.

% If a signal x(t) conincides with its reflection x(-t). we have

% x(t) = x(-t). This signal is symmetric with respect to time original 0

% While if a signal x(t) is conindides with is negative reflection -x(-t).

% This means the signal is nonsymmtric w.r.t time origin, we call it odd

% signal. So we always can decompose an arbitrary signal into even and odd

% parts. y(t) = y_e(t) + y_o(t). Then we can easily build them as

% y_e(t) = 1/2(y(t) + y(-t)); y_o(t) = 1/2(y(t) - y(-t))

% So, let us try to use these two definition to anlaysis the above example.

% and then, get the odd & even part of y(t)

[yo, ye] = oddeven(t, y);

figure(2)

subplot(211);

plot(t, yo, 'r');

title('odd part signal of y(t)')

grid

axis([min(t) max(t) -4 4])

subplot(212);

plot(t, ye, 'k')

title('even part signal of y(t)')

grid

axis([min(t) max(t) -2 7])

% Assignment 1.2

% If we have a new signal

% y(t) = 2 * ramp(t + 2.5) - 5 * ramp(t) + 3 * ramp(t - 2) + ustep(t-4)

% Please plot y(t), and extract its even & odd parts out.