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Assignment Help Answers with Step-by-Step Explanation:

X(f) = ∫[x(t) * e^(-j2πft)] dt from -∞ to ∞

Given x(t) = 3e^(-0.1t)u(t) (where u(t) is the unit step function), let's compute X(0):

x(n) = 3e^(-0.1n) for n = 0, 1, 2, ..., 99.

The adequacy of the number of samples depends on the specific application. If you need to accurately represent the signal x(t), you should choose a sufficient number of samples to capture its frequency components.

#include <fftw3.h>

#define N 100 // Number of samples

// Initialize x(n) with the given values

for (int n = 0; n < N; n++) {

fftw_execute(plan);

// X(0) is at index 0 in X

}

4. Plot and compare |X(0)| and |X(f)|:

Remember to include the necessary libraries for your chosen plotting method and adjust the code as needed for your specific environment.