# Discrete Signal processing

#### josh007

Joined Sep 20, 2015
43
Hi All,

Please can you correct me in my exam preparation questions: Are the below true or false.

I say question 13 above is TRUE since if there is a constant in the difference equation is no more Linear.

I say question 17 is FALSE since this applies for a system has MEMORY.

Am I correct in my 2 answers?

thank you

regards
Joshy

#### WBahn

Joined Mar 31, 2012
26,398
Your reasoning (or, more precisely, your stated justifications) are very weak. You justification for your answer to #13 implies that a system IS and LTI system as long as there are no constants in the difference equation. Is that true?

Your reasoning for #17 says that something applies to a system that has memory. So? What does that have to do with the price of tea in China? Your justification needs to address the claim that is made. For instance, let's say that the claim had been made that a parrot has feathers and you say that this is false because eagles have feathers. The fact that eagles have feathers does not mean than parrots can't have feathers. Similarly, the fact that a statement applies to a system that has memory does not mean that it can't apply to a system that is invertible. You have to show that the stated claim is not sufficient for the system to be invertible.

#### josh007

Joined Sep 20, 2015
43
Hi Wbahn,
You are correct my reasoning is nonsensical. But I am just trying to get help from you all to direct me on the correct path. From reading DSP in practice. Question 13. I will say is true? Am i correct in saying this? Because using the fact that a constant term should not be present in a LTI system difference equation or in the difference equation the coefficients should not be varying. Am i correct?

In question 13 I will say its false because an inverted system requires the unique output to determine the input. Am I correct? I just testing myself and since this past exam papers don't have model answers i will not know the answer.
Thank you

#### WBahn

Joined Mar 31, 2012
26,398
You are definitely on the right track now.

Remember that LTI means two things -- linear AND time-invariant. The time-invariant part requires that the system itself not be changing with time, hence all the coefficients must be constant, but this doesn't preclude the difference equation having an offset. The linear part requires that the system obey superposition, which can hold even if the coefficients are changing but which cannot hold if there is an offset (whether it is constant or not). But and LTI system must satisfy BOTH at the same time.

An invertible system requires, as you stated, that each input produce a single, unique output such that knowing the output tells you what the input was. The constraint that the output at any given time only depends on the input at that time does not impose this property.

#### josh007

Joined Sep 20, 2015
43
Hi Sir (Mr WBahn),

Thank you,

Wow so my answers are correct. Sir, I appreciate your time taken to guide me on a more detailed analysis.

regards
Joshy