Knowee
Questions
Features
Study Tools

A Digital filter with a 3dB bandwidth of 0.5π is to be designed from 1st orderanalog butterworth filter using BLT and obtain H(z

Question

A Digital filter with a 3dB bandwidth of 0.5π is to be designed from 1st order analog Butterworth filter using BLT and obtain H(z)

🧐 Not the exact question you are looking for?Go ask a question

Solution

To design a digital filter with a 3dB bandwidth of 0.5π using a 1st order analog Butterworth filter and the bilinear transform (BLT) method, follow these steps:

  1. Determine the transfer function of the 1st order analog Butterworth filter. The transfer function of a 1st order Butterworth filter is given by:

    H(s) = 1 / (s + ωc)

    where s is the Laplace variable and ωc is the cutoff frequency.

  2. Convert the transfer function from the Laplace domain to the z-domain using the bilinear transform. The bilinear transform is given by:

    s = 2/T * (1 - z^(-1)) / (1 + z^(-1))

    where T is the sampling period.

    Substitute the bilinear transform into the transfer function of the analog Butterworth filter:

    H(z) = H(s) |s = 2/T * (1 - z^(-1)) / (1 + z^(-1))

  3. Simplify the expression for H(z) by substituting ωc = 0.5π and rearranging the terms.

  4. Normalize the transfer function by dividing both the numerator and denominator by the coefficient of the highest power of z.

  5. Implement the digital filter using the simplified and normalized transfer function H(z).

By following these steps, you can design a digital filter with a 3dB bandwidth of 0.5π using a 1st order analog Butterworth filter and the bilinear transform method.

This problem has been solved

Similar Questions

What is the relation between Analog filter Frequency and digital filter Frequency when BLT Method is used for filter design ?

In BLT Method, Frequency Transformation from Analog Filter  to Digital Filter isSelect one:Many-to-ManyOne-to-ManyOne-to-OneMany-to-One

One of the zeros of a third order Linear Phase filter lies at z = -0.5. Findtransfer function and Impulse Response of the filter

The filter whose TF of the system is  isSelect one:a. All pass Filter  b. High pass Filterc. Band pass Filterd. Low pass Filter

One of the zeros of a third order Linear Phase filter lies at z = -0.5. Findtransfer function and Impulse Response of the filter.

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.