Lecture #10 - FIR Filter Design Flashcards
Why FIR filters?
- Inherently stable
- Can be designed to have linear phase or generalised linear phase
- Convenient/fast implementation
What are the FIR design methods?
- Windowing
- Optimisation approach -> Packs-McClellan method
- Exploit tools that implement algos for FIR filter design (MATLAB)
With an ideal frequency response, it will yield impulse that is non-causal, indefinitely long. How do you obtain an FIR?
By truncating the ideal response through the windowing method
What are two implications of windowing?
- A short window minimises calculations by affecting fewer samples, making it computationally efficient.
- Having the window’s frequency response closer to an impulse ensures that the window introduces minimal distortion in the frequency domain, improving the accuracy of the windowed signal’s representation compared to the ideal response.
Explain Gibbs phenomena
- Resultant oscillations in integral
- Oscillations increase as M increases but don’t change in amplitude
- Reduce effect with less abrupt truncation
- Taper window smoothly to zero at each end to reduce height of sidelobes
A rectangular function with abrupt transition in the frequency domain corresponds to what in the time domain
Translates to a sinc function of infinite duration in time domain
Truncation of this signal in the time-domain results in what
The Gibbs phenomena in the frequency domain
Discarded samples in time-domain means what in frequency doain
Missing frequencies
What does better choice of time-domain window mean?
It can improve but not remove Gibbs phenomena
A rectangular window has the narrowest what?
mainlobe
In Hann, Hamming, Blackman, what is the transition to 0
A smoother transition
- Reduces sidelobes
- But wider mainlobe
