LTI-filter, compute H(z) from freqz-response

  • Thread starter mkkribor
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In summary, an LTI-filter is a type of filter used in signal processing that is linear and time-invariant. To compute H(z) from a freqz-response, you can use the inverse z-transform. H(z) is significant in signal processing as it represents the relationship between input and output signals and is used in designing and implementing filters. It can be determined from other characteristics of a filter, but it has limitations as it assumes linearity and time-invariance and does not account for nonlinear effects.
  • #1
mkkribor
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Hi!

I have a problem i can't solve:

Compute the System Function H(z) from the Frequency

H(e^jw)=2e^(-j 3/2 w) 〖[cos(w/2)]〗^2


The answer should be in the form:
H(z)= (b_0+b_1 z^(-1)+b_2 z^(-2)+⋯)/(1-a_1 z^(-1)-a_2 z^(-2)-…)
where z = e^jw, and the b and a are constants.

Thx for any help!
 
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  • #2
I get to the point where:

H(e^[jw]) = e^[-j(w/2)] * (1 + 2e^[-jw] + e^[-j2w])

but then I am stuck..
 

FAQ: LTI-filter, compute H(z) from freqz-response

What is an LTI-filter?

An LTI-filter, or linear time-invariant filter, is a type of filter used in signal processing that has the property of being linear and time-invariant. This means that the output of the filter is a linear combination of the input signal and the filter's impulse response, and the filter's response does not change over time.

How do you compute H(z) from a freqz-response?

To compute H(z) from a freqz-response, you can use the inverse z-transform. This involves taking the inverse of the z-transform of the frequency response, which will give you the filter's transfer function in terms of z.

What is the significance of H(z) in signal processing?

H(z) is the transfer function of an LTI-filter, which represents the relationship between the input and output signals. It is used to analyze the frequency response of a filter and understand how it affects the input signal. It is also used in designing and implementing filters for specific signal processing applications.

Can H(z) be determined from other characteristics of a filter?

Yes, H(z) can be determined from other characteristics of a filter, such as its impulse response or frequency response. These can be used to calculate H(z) using mathematical formulas or algorithms.

Are there any limitations to using H(z) in signal processing?

While H(z) is a useful tool in signal processing, it does have some limitations. It assumes that the filter is linear and time-invariant, which may not always be the case in practical applications. Additionally, H(z) does not take into account any nonlinear effects that may occur in a filter.

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