OE-8.4 FIR Filter Design
You can design linear-phase FIR low-pass, high-pass, band-pass and band-stop filters using windows, and justify choosing FIR over IIR.
The FIR filter's selling point is exact linear phase, which means every frequency is delayed equally and the waveform shape survives - indispensable in data transmission and image processing. The window method is a controlled compromise: the window's main lobe sets transition width and its side lobes set stopband attenuation, and you cannot improve both without more taps. Keep the FIR/IIR comparison sharp, because it is the standard exam question and the standard real decision.
Work through these
Introduction to FIR filters
The first filter family, and the property it exists for. A finite response cannot be unstable, which is a strong guarantee.
Linear phase filters and their conditions
Exactly linear phase, and what the coefficients must satisfy to achieve it. Every frequency delayed equally means pulse shapes survive, which matters in data transmission.
Design of FIR filters using windows
The standard design route: take an ideal response and multiply by a window. The window choice is a trade between transition width and stopband depth.
Low-pass and high-pass FIR design
The two basic shapes, designed end to end. Doing both shows you that the second is a small transformation of the first rather than a new problem.
Band-pass and band-stop FIR design
The two composite shapes, built the same way. At this point the pattern should be doing the work rather than a new recipe each time.
Comparison between FIR and IIR filters
The choice you actually make in practice, stated as a trade. Phase linearity against filter order is the axis, and the next topic is the other side of it.
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