6. FIR Filters: Window Method of Design
The Window Method is a fundamental technique for designing Finite Impulse Response (FIR) filters, emphasizing the creation of filters based on desired frequency responses which are then truncated for practical implementation. It outlines the design process, including the choice of window functions that affect filter characteristics and application areas, such as audio and image processing. Overall, the method balances computational efficiency and filter performance through key trade-offs in design.
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What we have learnt
- The Window Method simplifies FIR filter design using ideal frequency responses and window functions.
- Various window functions, such as the Rectangular and Hamming windows, affect the filter's frequency response characteristics.
- The design process involves specifying the desired frequency response, computing the ideal impulse response, choosing a window function, and verifying the resulting filter's performance.
Key Concepts
- -- FIR Filter
- Finite Impulse Response filter characterized by a finite number of coefficients, yielding an output that is a weighted sum of recent input samples.
- -- Window Method
- A technique for designing FIR filters by applying a window function to an ideal impulse response to limit its length and reduce frequency response ripples.
- -- Ideal Frequency Response
- The desired characteristics of a filter, such as low-pass, high-pass, or band-pass, expressed mathematically through functions like the sinc function.
- -- Window Function
- A mathematical function applied to the ideal impulse response of a filter to diminish side-lobes and control the filter's characteristics.
- -- Tradeoffs in FIR Filter Design
- Considerations and compromises between factors like main-lobe width, side-lobe attenuation, filter length, and computational complexity when designing FIR filters.
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