Seonglae Cho2017143020 조성래
3.3
∴ the fundamental frequency is and
3.4
so Fourier coefficient is like this
because it is odd function
and is like this
3.6
(a). If Fourier coefficient has to be conjugate-symmetric like then signal is real
- for , so not a real valued ()
- for , so real valued
- for so real valued
(b). If Fourier coefficients is even, then a signal must be even. is even signal
3.7
According to differentiation property
According to given expression, when is 0
3.13
since is real and odd, is purely imaginary and odd. Therefore,
because it is odd function
which means when k is even, when k is odd
Corresponding LTI system output is like this
When k is even, is zero. When k is odd
so always
3.21
3.24
(a).
(b). let is Fourier series representation of then
because it is odd function
(c). and
3.26
(a). If is real, then and but it is not true. So is not real.
(b). Since , is even.
(c). so
Since it is not even, is not even