Question

Create a new MATLAB seript file and solve the followisg enereises: Fixerctes 1

a) Define the following continuous signaks. Assume −6≤t≤6 for all signals. Use a suitable increment value for t.
- s1​(t)=sin(2πt)
- s2​(t)=cos(4πt)
- s3​(t)=u(t)
- s4​(t)=2u(t−2)+u(t−3)
- s5​(t)=e²ᵗ
- s6​(t)=sin(t)/t (This is known as the siec function)

Answer 1

The exercise involves creating a MATLAB script to define and visualize six continuous signals within a specific time range using MATLAB. The script will include defining the time vector with a given increment and coding each signal using MATLAB's functions and operators, handling cases like the singularity in the sinc function.

Step-by-step explanation:

To create a new MATLAB script file and solve the exercise for defining continuous signals, you would start by defining the vector t that covers the range from -6 to 6 using a suitable increment. A common choice for the increment value in MATLAB might be 0.01 or 0.001 for a high-resolution plot of the continuous signals.

Here is an example of how you might define each signal within the script:

s1(t) = sin(2πt): Represents a simple sine wave oscillating at a frequency of 1 Hz.

s2(t) = cos(4πt): Represents a cosine wave oscillating at a frequency of 2 Hz.

s3(t) = u(t): Represents the unit step function, which is 0 for all t < 0 and 1 for all t ≥0.

s4(t) = 2u(t−2) + u(t−3): A piecewise function that changes values at t=2 and t=3.

s5(t) = e²2ᵗ: An exponentially increasing function dependent on the variable t.

s6(t) = sin(t)/t: Also known as the sinc function, which needs special handling at t=0 to avoid division by zero.

The MATLAB code snippet may look like this:

t = -6:0.01:6;

s1 = sin(2 * pi * t);

s2 = cos(4 * pi * t);

s3 = double(t ≥ 0);

s4 = 2 * double(t ≥ 2) + double(t ≥ 3);

s5 = exp(2 * t);

s6 = sin(t) ./ t;

s6(t == 0) = 1; % Handling the singularity at t=0

Then, you would use MATLAB functions such as plot to visualize these signals.