What the syllabus asks you to cover
IIR filter design by classical filter design. IIR filter design by Impulse-invariant method, IIR low pass discrete filter design. FIR filter design by Fourier approximation. FIR filters using window function, Design of linear phase FIR filter by the frequency sampling method, FIR filter design using the Remez exchange algorithm. Design of optimum equi-ripple linear-phase FIR filters.
Start here for the core ideas. A dedicated GitBook topic page was not available; this original guide is introductory. Use the syllabus checklist and references below to study the remaining details.
Begin with specifications
A filter design starts with passband, stopband, allowable ripple, attenuation and transition width. Sampling frequency determines the conversion between hertz and normalized digital frequency. FIR and IIR are classifications of the impulse response, not simply labels for particular implementation software.
Choose the design method
An FIR filter can have exact linear phase when its coefficients have suitable symmetry or antisymmetry. Windowing truncates an ideal impulse response and trades transition width against ripple. Equiripple methods distribute approximation error according to a chosen objective. IIR methods often start from an analog prototype; impulse invariance and the bilinear transform introduce different frequency-domain effects.
Try it
At a 10 kHz sampling rate, 1 kHz corresponds to radians/sample. Mixing hertz with radians/sample is a common design error.
Check your understanding
Why does an ideal sharp cutoff require an impractical impulse response? Compare FIR length with IIR order for a stated specification, and check stability after coefficient quantization.
Pause and recall
Without looking back, explain the main idea, recall a key definition or formula, and describe when it applies. Include assumptions and units where relevant. Revisit any step you could not explain.