Frequency response and Impulse Response

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SUMMARY

The discussion focuses on calculating the transfer function, frequency response, and impulse response of a discrete-time system defined by the difference equation y(n) + 1/8y(n-1) - 5/8y(n-2) = 1/2x(n-1). The transfer function derived using the z-transform is H(z) = (1/2)z^(-1) / (1 + (1/8)z^(-1) - (5/8)z^(-2)). The user seeks guidance on how to derive the frequency response and impulse response from this transfer function, as well as the relationship between impulse response and frequency response in both the s and z domains.

PREREQUISITES
  • Understanding of z-transform and its applications in discrete-time systems
  • Knowledge of transfer functions and their significance in system analysis
  • Familiarity with frequency response and impulse response concepts
  • Basic grasp of difference equations in signal processing
NEXT STEPS
  • Learn how to derive frequency response from a transfer function using H(e^(jω))
  • Study the calculation of impulse response from the transfer function using inverse z-transform
  • Explore the relationship between impulse response and frequency response in the z-domain
  • Investigate the properties of the Dirac delta function in the context of z-transform
USEFUL FOR

Signal processing students, control system engineers, and anyone involved in analyzing discrete-time systems and their responses.

Cossie
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Im struggling to do the following question. Any help would be appreciated

A following system has the following difference equation

y(n)+ 1/8y(n-1) - 5/8y(n-2)=1/2x(n-1)

First part is to calculate the system transfer function using the z transform. Then get the frequency response and the impulse

Ive managed to work out the system function and using the z transform it equates to
\frac{Y(z)}{X(z)}=\frac{1/2z^{-1}}{1+1/8z^{-1}-5/8z^{-2}}

From this how do i calculate the frequency response and the impulse response of the system.

Many thanks
 
Physics news on Phys.org
What is the z transform of δ(t), the Dirac delta (impulse) step function?

What is the relationship between a network's impulse response and its frequency response?
(Either in the s or z domain?).
 

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