Understanding Convolution with Letters: Tips for Overlapping Inputs

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SUMMARY

The discussion focuses on the convolution of discrete signals represented by delta functions, specifically h[n] = δ[n-a] + δ[n-b] and x[n] = δ[n-c] + δ[n-d]. The convolution result is expressed as y[n] = h[n]*x[n]. Participants seek clarification on how to visualize the overlap of the delta functions represented by letters, particularly when determining the conditions under which a and b overlap with c and d. The importance of defining the delta function, δ[k], is emphasized for a complete understanding of the convolution process.

PREREQUISITES
  • Understanding of discrete-time signals and systems
  • Familiarity with the convolution operation in signal processing
  • Knowledge of delta functions and their properties
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the properties of the delta function, δ[n]
  • Learn about the graphical representation of convolution
  • Explore the implications of overlapping signals in convolution
  • Practice convolution with various discrete signals using MATLAB or Python
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Students and professionals in signal processing, electrical engineering, and anyone looking to deepen their understanding of convolution operations involving discrete signals.

noname1
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convolve the following

h[n] = δ[n-a] + δ[n-b]
x[n] = δ[n-c] + δ[n-d]

i understand that the convolution is y[n] = h[n]*x[n] and i know how to do it with number instead of letters however not quite sure how it would work with the letters, its not possible to view when a & b will overlap c & d.

Any help would be appreciated
 
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What is your definition of ##\delta[k]##? When you say you understand ##y[n] = h[n]*x[n]##, what,exactly, do you understand? In other words, what would be the actual formula for ##y[n]##?
 

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