Lecture 17: FIR Design by Windowing, Kaiser Window & Optimal Approximation
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چکیده
The FIR techniques are based purely in discrete-time, unlike the previous techniques for IIR design that were designed from the transformation of filters specified in continuous time. Recall ideal LPF H(e jω) = 1 |ω| < ω c 0 else and h d [n] = sin ω c n πn ∀n What happens if we just truncate h d [n] to a finite of samples? h[n] = h d [n] −M ≤ n ≤ M 0 else It is equivalent to convolution in frequency domain of a sinc function and a rectangle function. General case: h[n] = h d [n] 0 ≤ n ≤ M 0 else or could multiply it by some " window " function h[n] = h d [n]w[n] (17.1) When the window is rectangle w[n] = 1 0 ≤ n ≤ M 0 else then H(e jω) = 1 2π π −π H d (e jθ)W (e j(ω−θ))dθ which is a periodic convolution between H d (e jω) and W (e jω) and can be thought of as smearing. Key idea: lots of different window functions w[n], each with different properties.
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