Calculating the frequency response of filter with a matrix

In summary, the conversation discusses a homework question that involves forming equations to create a matrix and solving it using Matlab. Part 3 of the question involves calculating the frequency response by finding the ratio of Vout and Vin, represented by v3 and v0 respectively. The conversation suggests replacing resistor values with impedance values, but this may not work since the frequency is unknown. It is suggested to calculate the frequency response for multiple frequencies to create a graph, and the same equations used for previous parts can be used for this calculation.
  • #1
Dethoven
13
0

Homework Statement


This is actually part 3 of the question. Part one was to form 7 equations to form a 7x7 matrix, part 2 was to solve it, which I've done. This question is to be done with Matlab, by the way.
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Part 3:
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Homework Equations


Frequency response = Vout / Vin.

The Attempt at a Solution


I know the frequency response is the ratio of Vout and Vin, in this case, v3 and v0, I'm not sure how to incorporate that with the matrix I have. I could replace the resistor values with the impedance of the corresponding elements, but since the frequency is unknown, that wouldn't work. I've calculated frequency responses before, but that was for simpler circuit in which I could use the potential divider formula.
 
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  • #2
calculating the frequency response at one frequency would get you one one point of the graph.
What if you compute 10 different frequencies?
What if you compute 100?
or 1000?

you can still use the same equations you used for the previous parts.

By the way you might want to show everyone the equations you got
 

1. What is the frequency response of a filter?

The frequency response of a filter is a mathematical representation of how a filter affects different frequencies in a signal. It shows the magnitude and phase response of the filter at different frequencies.

2. How is the frequency response of a filter calculated?

The frequency response of a filter can be calculated by taking the Fourier transform of the filter's impulse response. This results in a transfer function, which represents the filter's frequency response in the form of a complex function.

3. What is the significance of using a matrix in calculating the frequency response of a filter?

A matrix is used to represent the coefficients of the filter's transfer function. This allows for an efficient and organized way of calculating the frequency response, as well as making it easier to analyze and manipulate the filter's characteristics.

4. How does the size of the matrix affect the accuracy of the frequency response calculation?

The size of the matrix used to calculate the frequency response does not necessarily affect the accuracy of the calculation. However, using a larger matrix can result in a more detailed and precise representation of the filter's frequency response.

5. Can the frequency response of a filter be modified by changing the values in the matrix?

Yes, the frequency response of a filter can be modified by changing the values in the matrix. The coefficients in the matrix correspond to the filter's transfer function, so altering these values will result in a change in the filter's frequency response.

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