PHYSICS 3K03 Final: 359_Summary
15 Sep 2017
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General complex exponential signal (continuous): r>0: growing r<0: decaying. Periodicity if (x[n] is periodic if is rational) Harmonically related complex exponentials (sets of periodic exponentials with a common period t0): Common period n frequencies are multiples of . Note: there are only n distinct periodic exponentials in the set. Define: ( is the response of the shifted unit impulse. The responses of a time-invariant system to the time- shifted unit impulses are simply time-shifted versions of one another. Lti systems are fully described by their impulse response. Relationship between lti system properties and the impulse response. Fourier series representation of periodic signals as weighted superposition of complex exponentials. Convolution with impulse response h(t) and h[n] is replaced by multiplication with eigenvalues and. En = 0 does not imply that xn(t) equals x(t) for every value of t. but: difference between xn(t) and x(t) has zero energy ). Xn(t) and x(t) are indistinguishable for physical systems.
