Which of the following is the first method proposed for design of FIR ...
Explanation: The design method based on the use of windows to truncate the impulse response h(n) and obtaining the desired spectral shaping, was the first method proposed for designing linear phase FIR filters.
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Which of the following is the first method proposed for design of FIR ...
The correct answer is option 'C', the windowing technique.
The windowing technique is the first method proposed for designing Finite Impulse Response (FIR) filters. FIR filters are digital filters with finite impulse response, meaning they produce an output based only on a finite number of input samples. The windowing technique is commonly used to design FIR filters because of its simplicity and flexibility.
Here is a detailed explanation of the windowing technique for designing FIR filters:
1. Introduction to FIR Filters:
- FIR filters are a type of digital filter that have linear phase characteristics.
- They have a finite length impulse response, which means they have a finite number of coefficients.
2. Need for Windowing Technique:
- In FIR filter design, an ideal frequency response is desired, which is typically not achievable due to practical limitations.
- The ideal frequency response can be approximated by truncating the impulse response of an infinite impulse response (IIR) filter.
- However, truncation of the impulse response leads to undesired effects such as ripples in the frequency response and longer transient response.
- The windowing technique is used to minimize these effects and improve the overall performance of the FIR filter.
3. Working of Windowing Technique:
- The windowing technique involves multiplying the truncated impulse response by a window function.
- The window function is a symmetric function that smoothly tapers the truncated impulse response towards zero at the edges.
- This tapering reduces the ripples in the frequency response and improves the transient response of the FIR filter.
4. Types of Window Functions:
- There are various types of window functions that can be used, such as the Hamming window, Hanning window, Blackman window, etc.
- Each window function has different characteristics and trade-offs in terms of frequency response and transient response.
5. Design Procedure:
- The design procedure for FIR filters using the windowing technique involves the following steps:
- Specify the desired frequency response.
- Determine the length of the filter and the number of coefficients.
- Choose an appropriate window function.
- Calculate the impulse response of the ideal filter.
- Truncate the impulse response to the desired length.
- Multiply the truncated impulse response by the chosen window function.
- Normalize the filter coefficients to achieve the desired gain.
By using the windowing technique, FIR filters can be designed with improved frequency response and transient response characteristics. This method is widely used in various applications such as audio processing, image processing, and communication systems.
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