FIR filters, impulse responses and unit step function

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SUMMARY

The discussion centers on the evaluation of expressions involving the discrete delta function δ[n] and the unit step function u[n]. The expressions presented include A. u[n-m] = δ[n] + u[n-m+1], B. x[n]δ[n-m] = x[n-m], C. δ[n] = u[n] - u[n-1], and D. δ[n]δ[n-m] = 0. The incorrect expression identified is A, as it misrepresents the relationship between the unit step function and the delta function. The correct interpretation of these functions is crucial for understanding signal processing concepts.

PREREQUISITES
  • Understanding of discrete-time signals and systems
  • Familiarity with the properties of the delta function δ[n]
  • Knowledge of the unit step function u[n]
  • Basic concepts of convolution in signal processing
NEXT STEPS
  • Study the properties of the delta function and unit step function in detail
  • Learn about convolution and its applications in signal processing
  • Explore the implications of incorrect expressions in signal analysis
  • Investigate FIR filter design and its relationship with impulse responses
USEFUL FOR

Students and professionals in signal processing, electrical engineering, and anyone involved in the analysis of discrete-time systems will benefit from this discussion.

Jd303
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Hey everyone, the question I am faced with is this:

Which of the following expressions involving δ[n] is incorrect?
where "m" is a non zero integer and u[n] is the unit step function.

A. u[n-m] = δ[n] + u[n-m+1]

B. x[n]δ[n-m] = x[n-m]

C. δ[n] = u[n] - u[n-1]

D. δ[n]δ[n-m] = 0

I have been scratching my head for a while, but really not sure what to do. Any help as always would be greatly appreciated!
 
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Hey Jd, take a shot at each of these, explain your rationale & then maybe we can be of help.
 

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