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Modellierung 1

What is a continuous-time signal?

A function with an analytical representation eg y(x)=sin(x)

Modellierung 1

What is an odd function?

f(x)=-f(-x)

eg x^3, sin(x)

Modellierung 1

What is an even function?

f(x)=f(-x)

eg x^2 or cos(x)

Modellierung 1

What does it mean if a function has compact support?

It is zero everywhere outside of a fixed interval.

Modellierung 1

What is a discrete-time signal?

A signal where we save values only for discrete points. Notation: f[n]

Modellierung 1

What is a periodic signal?

f(x - k*T) = f(x), k=...-1,0,1,...

Modellierung 1

How does one create a periodic signal out of an aperiodic one?

g(x) = ... + f(x-T) + f(x) + f(x+T) + ...

Modellierung 1

When is an operator L linear?

L{ax+by}=aLx+bLy

Modellierung 1

What's a shift-invariant system?

y[n] = f{x[n]} => y[n+k] = f{x[n+k]} für alle k

Modellierung 1

What's a hermite function?

a function with complex domain, satisfying f(x) equals the complex conjugate of f(-x)

Modellierung 1

What is the impulse signal?

A function which is 0 everywhere, except at x=0, but the integral from - to + infinity is 1. Technically not a function, but a distribution. Can be considered the limit of w approaching 0 of a gaussian of width w or a function which is 1/w for the interval from 0 to w and 0 else.

Modellierung 1

Was ist der Rayleigh Quotient und was nützt er?

(r^T S r) / (r^T r)

Wird maximiert oder minimiert von r als zum größten oder kleinsten Eigenwert von S gehörender Eigenvektor.

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