Flashcards on Finite Impulse Response (FIR) Filters
FIR Filters Explained: Design, Properties & Examples
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FIR Filter Design
26 cards
Card 1
Question: What symmetry property of FIR filters reduces the number of multiplications required for implementation?
Answer: Symmetric FIR filters (coefficients satisfy g[n]=g[M−n]) allow using filter symmetry to save about half the multiplications.
Card 2
Question: What is the general approach to design an FIR filter directly from a desired frequency response?
Answer: Start with the desired frequency response Ĝ(Ω), derive the corresponding unit impulse response g[n] via the inverse DTFT (analytical or numerical int
Card 3
Question: Write the inverse DTFT expression used to obtain the FIR impulse response from a desired frequency response Ĝ(Ω).
Answer: g[n] = (1/2π) ∫_{−π}^{π} Ĝ(Ω) e^{jΩn} dΩ (or a numerical integration when analytic evaluation isn't possible).
Card 4
Question: When designing an ideal low-pass FIR filter, what two practical problems arise with the impulse response obtained from the inverse DTFT?
Answer: Problem 1: The ideal impulse response is not time-limited (infinite length), so it must be truncated. Problem 2: The impulse response is non-causal, s
Card 5
Question: How is the impulse response of an ideal low-pass filter expressed before truncation and shifting?
Answer: The ideal low-pass impulse response is a sinc function: g[n] ∝ sinc(nΩ_C/π) (obtained from integrating the rectangular frequency response with cutoff
Card 6
Question: What effect does truncating the ideal FIR impulse response (i.e., finite-length sampling) have on the filter's frequency response?
Answer: Truncation introduces approximation error and causes the Gibbs phenomenon (overshoot and ripples) at points of discontinuity in the frequency response
Card 7
Question: What straightforward method is used to reduce Gibbs phenomenon effects when designing FIR filters by truncation?
Answer: Apply windowing: multiply the truncated impulse response by a suitable window (e.g., rectangular, Hamming, Blackman, Kaiser, Hann, triangular) to impr
Card 8
Question: How does increasing the number of samples (filter length) affect the frequency response approximation of an FIR filter designed by truncation?
Answer: Increasing the number of samples improves the approximation to the ideal frequency response, reducing the width of transition bands and overall error,
Card 9
Question: List key advantages of FIR filters mentioned in the content.
Answer: Advantages: inherently stable (no recursion), can have linear phase when symmetric (constant group delay), design directly from desired frequency resp
Card 10
Question: What is the main disadvantage of FIR filters compared to IIR filters as stated in the content?
Answer: To achieve comparable selectivity, FIR filters typically require a much higher order (often tens or more), meaning longer filter length.