Signals and Systems Oppenheim English Edition Answers Chapter 3Chapter 3 Answers31 Using the Fourier series synthesis eq 33832 Using the Fourier series synthesis eq 39533 The given signal is Form th

nt is . Thus, we have

Using the orthogonality property of complex exponentials, we can find as follows:

Thus, the Fourier series coefficients of x(t) are given by:

Using the Fourier series synthesis equation, we can express x(t) as:

3.9 We can express x(t) as a sum of two periodic signals:

where and are the Fourier series coefficients of and , respectively. Using the given information, we have:

Thus, the Fourier series coefficients of x(t) are given by:

Using the Fourier series synthesis equation, we can express x(t) as:

3.10 We can express x(t) as a sum of two periodic signals:

where and are the Fourier series coefficients of and , respectively. Using the given information, we have:

Thus, the Fourier series coefficients of x(t) are given by:

Using the Fourier series synthesis equation, we can express x(t) as:

3.11 We can express x(t) as a sum of two periodic signals:

where and are the Fourier series coefficients of and , respectively. Using the given information, we have:

Thus, the Fourier series coefficients of x(t) are given by:

Using the Fourier series synthesis equation, we can express x(t) as