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What is the kind of relationship between Ω and ω?

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What is the kind of relationship between Ω and ω?

(a) Many-to-one

(b) One-to-many

(c) One-to-one

(d) Many-to-many

The question was posed to me in an interview for job.

The doubt is from Bilinear Transformations topic in division Digital Filters Design of Digital Signal Processing

1 Answer

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Right answer is (c) One-to-one

Explanation: The analog frequencies Ω=±∞ are mapped to digital frequencies ω=±π. The frequency mapping is not aliased; that is, the relationship between Ω and ω is one-to-one. As a consequence of this, there are no major restrictions on the use of bilinear transformation.

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