Question

Low pass Butterworth filters are:

• A. All-zero filters
• B. Pole-pole filters
• C. All-pole filters
• D. Pole-zero filters

Hint:

- Butterworth filters are all-pole filters, meaning they have poles but no finite zeros. - Their primary characteristic is a maximally flat magnitude response in the passband.

Answer 1

The Correct Option is C

Step 1: Understanding Butterworth Filters
- The Butterworth filter is a type of low-pass filter that provides a maximally flat magnitude response in the passband.
- It is designed to minimize ripples and ensure a smooth frequency response.
Step 2: Pole and Zero Characteristics
- The transfer function of a Butterworth filter is derived in such a way that: \[ H(s) = \frac{1}{\prod_{k=1}^{N} (s - p_k)} \] where \( p_k \) are the poles of the filter.
- Butterworth filters have no finite zeros, meaning they are all-pole filters.
Step 3: Evaluating the Options
- (A) Incorrect: Butterworth filters are not all-zero filters, as they contain only poles.
- (B) Incorrect: The term pole-pole filters is not a standard classification.
- (C) Correct: Butterworth filters have only poles and no finite zeros, making them all-pole filters.
- (D) Incorrect: A pole-zero filter contains both poles and zeros, which is not the case for Butterworth filters.