Signal generation in MATLAB ustep and ramp (discrete) + odd and even fucntion

Lab 2: Signal generation % How can we generate a discrete signal 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 % part11ar 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.

[KALYAN ACHARJYA]

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