1 Determine the convolution between two signals given below by using manual calculation. Show your calculation and illustrate graphically the resulting signal.

2 Write a MATLAB program (m-file) to determine the convolution between the two signals. Show your MATLAB programming code (in the appendix) and plot your results.

Sol12:

1. Manual Calculation: To determine the convolution between two signals f(t) and g(t), we need to perform the following steps:

Step 1: Flip one of the signals, say g(t), to get g(-t). Step 2: Shift the flipped signal g(-t) by the value of t, and multiply it with the other signal f(t). Step 3: Integrate the product obtained in Step 2 over all values of t.

Using the above steps, the convolution between f(t) and g(t) can be represented as:

f(t)*g(t) = ?f(t)g(t-t)dt

where * denotes convolution.

Let's apply these steps to find the convolution between the given signals:

f(t) = u(t) - u(t-1) g(t) = 2u(t) - u(t-2)

where u(t) is the unit step function.

Step 1: Flip g(t) to get g(-t):

g(-t) = 2u(-t) - u(-t+2) = 2u(-t) - u(t-2)

Step 2: Shift the flipped signal g(-t) by the value of t, and multiply it with f(t):

h(t) = f(t)*g(t) = ?[u(t)-u(t-1)][2u(t-t)-u(t-t-2)]dt = ?[2u(t-t)-2u(t-t-1)-u(t-t-2)+u(t-t-3)]dt

Step 3: Integrate the product obtained in Step 2 over all values of t:

For t

For 0 = t

For 1 = t

For t = 2: h(t) = ?[2u(t-t)-2u(t-t-1)-u(t-t-2)+u(t-t-3)]dt = - (t-2)u(t-2) + (t-3)u(t-3)

1. MATLAB Code: To determine the convolution between two signals using MATLAB, we can use the conv() function. The syntax for the conv() function is:

y = conv(f, g)

where f and g are the two input