Pole-zero analysis for stability in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function that finds poles and zeros of a system.

Signal Processing

from scipy.signal import [1]

Drag options to blanks, or click blank then click option'

Atf2zpk

Blfilter

Cfreqz

Dbutter

Attempts:

3 left

💡 Hint

Common Mistakes

Using filter design functions like butter instead of tf2zpk.

Importing freqz which computes frequency response, not poles and zeros.

The tf2zpk function returns zeros, poles, and gain of a transfer function.

2fill in blank

medium

Complete the code to find poles of the system given numerator and denominator coefficients.

Signal Processing

zeros, poles, gain = tf2zpk(num, [1])

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Aden

Bnum

Cgain

Dpoles

Attempts:

3 left

💡 Hint

Common Mistakes

Passing numerator coefficients twice.

Confusing gain or poles variable as input.

The denominator coefficients den define the poles of the system.

3fill in blank

hard

Fix the error in the code to check if all poles are inside the unit circle for stability.

Signal Processing

is_stable = all(abs(p) [1] 1 for p in poles)

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A>

B<

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < which checks for instability.

Using >= or <= which includes poles on the unit circle (marginally stable).

For discrete systems, stability requires all poles to have magnitude less than 1.

4fill in blank

hard

Fill both blanks to create a dictionary of poles and zeros magnitudes.

Signal Processing

magnitudes = {'poles': [abs(p) for p in [1]], 'zeros': [abs(z) for z in [2]]}

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Apoles

Bzeros

Cnum

Dden

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing numerator or denominator coefficients instead of poles or zeros.

Swapping poles and zeros variables.

We calculate magnitudes of poles and zeros from their respective lists.

5fill in blank

hard

Fill all three blanks to filter stable poles and zeros with magnitude less than 1.

Signal Processing

stable_poles = [p for p in [1] if abs(p) [2] 1]
stable_zeros = [z for z in [3] if abs(z) [2] 1]

Drag options to blanks, or click blank then click option'

Apoles

B<

Czeros

Dden

Attempts:

3 left

💡 Hint

Common Mistakes

Using denominator coefficients instead of poles or zeros.

Using greater than sign which selects unstable poles or zeros.

We select poles and zeros with magnitude less than 1 to identify stable ones.