... asck1NNÀ1n0xneÀjk2p=Nn: 4:4 :2These Fourier coefficients form a periodic sequence of fundamental period N suchthatckiN ck, 4:4 :3152FREQUENCY ANALYSISwhere i is an ... 4:4 :5Thus the frequency range for a discrete-time signal is unique over the range (Àp, p)or(0,2p). For real-valued x(n), X! is complex-conjugate symmetric. That is,XÀ!XÃ!: 4:4 :6Similar ... is,Y!H!X!, 4:4 :8where X! and Y! are the DTFT of the input x(n) and output y(n),respectively.Similar to (4.3.18),we can express X! and Y! asX!jX!jejfx!, 4:4 :9aY!jY!jejfy!:...