# Electr. Engineering - Digital Sig. Processing

1. Sep 4, 2007

### DefaultName

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.

$$x(t)$$ is random input and $$y(t)$$ is the output of $$x(t)$$

For Eq1:

$$y(t) = |x(t)| = \left\{ \begin{array}{l} x(t)\; \mathrm{if}\, x(t) \geq 0 \\ -x(t)\; \mathrm{if}\, x(t) < 0 \end{array}\right.$$

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:

$$y(t) = \int_0^t\lambda x(\lambda)d\lambda$$

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*

Last edited: Sep 4, 2007
2. Sep 5, 2007

### learningphysics

Both your answers look good to me. By the way, it's "causal" not "casual".

3. Sep 5, 2007

### DefaultName

Hahha, I just realized that. Wow.

Thanks tho.

4. Sep 5, 2007

### DefaultName

Now, Eq1 is obviously linear, but when I graph eq2, it seems to be nonlinear... does that make sense?

Last edited: Sep 5, 2007
5. Sep 5, 2007

### chroot

Staff Emeritus
Yes.

- Warren

6. Sep 5, 2007

### user101

is it because when you take derivatives and integrals, the terms will become nonlinear

also, in the one DefualtName posted, for equation 2, would that be a time varying or time invariant one. i would say varying because the actual output will be different from the input

Last edited: Sep 5, 2007