Week 2 Summary

One topic covered on Tuesday was energy. Energy says very little about peak magnitude, but both are important consideration. Energy is a norm with p=2, the Integral is normal of absolute value. The Infinite Norm returns the maximum value or the essential supremum. Power is the norm per unit of time. Watts are Joules per second. We discussed different types of signals such as the unit step and the unit pulse. Another function covered was the delta function which is a sifting function which makes it good for taking one time value out of the signal. Next we covered signal decomposition which involves using the delta function to break the signal into pieces that can be worked with. The continuous time delta function presents challenges because we aren’t able to have something that integrates over all time to 1.

The next day we discussed complex sinusoids as spirals in 3D space for a continuous time signal and a sampled version of dots for discrete time. We also discussed how although all continuous time sinusoids are periodic, not all discrete time sinusoids are periodic. The next major theme related plotting complex exponential signals as points in the complex plane with the real part signifying the exponential behavior of the signal and the imaginary part dictating the sinusoidal behavior. For continuous time we use Cartesian coordinates but in discrete time we use polar coordinates because we are only concerned with the –pi to pi range. Finally we discussed how systems are operators that act on signals. There are four different classifications of systems linear, nonlinear, time-invariant, and time-varying.

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