(adsbygoogle = window.adsbygoogle || []).push({}); Determine if the CT systems are 1) casual or uncasual 2) memory or memoryless.

Definitions:

Casual: If for any time t1, the output response y(t1) at time t1 resulting from input x(t) does not depend on the values of the input x(t) for t > t1.

Memory: If the output at time t1 depends in general on the past values of the input x(t) for some range of values of t up to t=t1.

[tex]x(t)[/tex] is random input and [tex] y(t)[/tex] is the output of [tex]x(t)[/tex]

For Eq1:

[tex]y(t) = |x(t)| = \left\{ \begin{array}{l}

x(t)\; \mathrm{if}\, x(t) \geq 0 \\

-x(t)\; \mathrm{if}\, x(t) < 0

\end{array}\right.

[/tex]

I said this system is CASUAL and MEMORYLESS.

- Casual - because at time t, y(t) will depend only t from the input function x(t), not some other arbitrary t value.
- Memoryless - because the outputs at time t do not depend on previous inputs.

For Eq 2:

[tex]y(t) = \int_0^t\lambda x(\lambda)d\lambda[/tex]

I said this system is CASUAL and has MEMORY.

- Casual - because at time t, it doesn't really depend on the future. It only depends on the past, so I'm guessing casual. *This I'm not too sure about*
- Memory - because the outputs at time t do depend on previous inputs since youre taking the integral from 0 to time t. *I'm almost sure about this one*

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# Homework Help: Electr. Engineering - Digital Sig. Processing

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