Bilinear Transformation is used for transforming an analog filter to a...
Explanation: The bilinear transformation can be regarded as a correction of the backward difference method. The bilinear transformation is used for transforming an analog filter to a digital filter.
View all questions of this test
Bilinear Transformation is used for transforming an analog filter to a...
Bilinear Transformation for Analog to Digital Filter Transformation
The statement "Bilinear Transformation is used for transforming an analog filter to a digital filter" is true. The bilinear transformation is a widely used method in digital signal processing to convert analog filters into their digital counterparts. Let's understand the concept in detail:
1. Analog Filters and Digital Filters:
- An analog filter is a device or circuit that processes analog signals or continuous-time signals.
- A digital filter, on the other hand, operates on discrete-time signals, which are represented as a sequence of samples or numbers.
2. Need for Analog to Digital Filter Conversion:
- In many practical applications, it is necessary to convert an analog filter into a digital filter. This is because digital signal processing offers several advantages over analog signal processing, such as easier implementation, flexibility, and the ability to handle complex algorithms.
3. Bilinear Transformation:
- The bilinear transformation is a mathematical technique used to convert the transfer function of an analog filter into its digital equivalent.
- It maps the complex s-plane (analog domain) onto the z-plane (digital domain) using a bilinear conformal mapping.
- The mapping is achieved by substituting s with a function of z in the transfer function of the analog filter.
4. Mapping of Frequency Response:
- The bilinear transformation not only maps the transfer function but also maps the analog filter's frequency response to the digital filter's frequency response.
- The frequency warping effect occurs due to the non-linear mapping of the s-plane to the z-plane.
- The frequency warping can cause distortion in the frequency response, especially at higher frequencies.
5. Advantages of Bilinear Transformation:
- The bilinear transformation method preserves the stability of the analog filter during the conversion process.
- It provides a one-to-one correspondence between the poles of the analog filter and the poles of the digital filter.
- The method is relatively simple and straightforward to implement.
- The resulting digital filter closely approximates the frequency response of the original analog filter.
Conclusion:
The bilinear transformation is a powerful technique used in digital signal processing to convert analog filters into their digital counterparts. It allows the preservation of stability and provides a close approximation of the analog filter's frequency response. Hence, the statement "Bilinear Transformation is used for transforming an analog filter to a digital filter" is true.
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).