Frequency Response of 3-Point Averaging System

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SUMMARY

The discussion focuses on determining the frequency response of a 3-point averaging system defined by the equation y[n] = (x[n] + x[n-1] + x[n-2]) / 3. Participants emphasize the importance of finding the impulse response and understanding the fundamental period, which is calculated as 2π/T, where T represents the fundamental period. The main goal is to derive the amplitude and phase of the output when a unit-amplitude sinusoidal input is applied.

PREREQUISITES
  • Understanding of discrete-time signals and systems
  • Familiarity with impulse response and frequency response concepts
  • Knowledge of sinusoidal inputs in signal processing
  • Basic skills in graphing functions and interpreting their characteristics
NEXT STEPS
  • Study the derivation of impulse response for discrete-time systems
  • Learn about calculating frequency response using the Z-transform
  • Explore the concept of fundamental period in signal processing
  • Investigate the effects of different input signals on system output
USEFUL FOR

Students and professionals in electrical engineering, signal processing enthusiasts, and anyone involved in analyzing discrete-time systems and their frequency responses.

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Homework Statement



y[n]= (x[n]+x[n-1]+x[n-2]) / 3 is the input output relationship

Homework Equations



Find the Frequency response.

The Attempt at a Solution



Ok I am very aware that I can easily find the impulse response and graph this and I can even get the general format for the frequency response, however how doyou figure out the fundamental period? I know its 2pi/T, where T is the fund. period but I don't see how I can graph x[n], y[n], or find the period
 
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I don't see why you need the fundamental period (whatever that means in this situation). Sounds like they just want the amplitude, and possibly the phase, of the output given a unit-amplitude, sinusoidal input.
 

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