Question

This question requires you to program in matlab

Design of a lowpass filter by pole-zero placement: By placing poles and zeros based on what
you have seen so far, and by trial and error, design a lowpass filter that satisfies the following:

The magnitude response is at least -3 dB in the frequency range 0 to 1000 Hz.

Answer 1

To design a lowpass filter using pole-zero placement in MATLAB, you can use the 'zpk' function to specify the poles and zeros. Start by determining the desired cutoff frequency, which in this case is 1000 Hz. Then, use the 'zpk' function to create a lowpass filter object with the desired poles and zeros. Finally, use the 'bode' function to visualize the magnitude response of the filter.

Step-by-step explanation:

To design a lowpass filter using pole-zero placement in MATLAB, you can use the 'zpk' function to specify the poles and zeros. Start by determining the desired cutoff frequency, which in this case is 1000 Hz. Convert the frequency to radians per second by multiplying by 2*pi. Then, use the 'zpk' function to create a lowpass filter object with the desired poles and zeros. Finally, use the 'bode' function to visualize the magnitude response of the filter and make adjustments as necessary.

Here's an example code snippet:

sampling_rate = 2000; % Hz

% Convert cutoff frequency to radians per second
cutoff_freq = 1000; % Hz
cutoff_freq_rad = cutoff_freq * 2 * pi;

% Create lowpass filter using pole-zero placement
[z, p, k] = butter(6, cutoff_freq_rad, 's');
sys = zpk(z, p, k);

% Visualize the magnitude response
bode(sys);