What the syllabus asks you to cover
Implementation of digital filter, Applications of FFT algorithms.
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.
Connect algorithms with implementations
A digital filter computes a specified transformation on a sequence. Time-domain convolution is direct and intuitive for short filters. Frequency-domain methods use DFT multiplication and an FFT algorithm to accelerate sufficiently large problems. An FFT is an algorithm for computing a DFT, not a different transform.
Handle block boundaries
Overlap-add and overlap-save manage the circular-convolution behavior of block FFT processing so that the desired linear-convolution output is recovered. The transform length, filter length and block size must be chosen consistently. Filter latency and computational cost matter as well as operation count.
Try it
A length-5 FIR filter convolved with a length-8 block produces 12 linear-convolution samples. An FFT method therefore needs a transform length of at least 12; a convenient larger length may be faster in a particular implementation.
Check your understanding
When might direct convolution be preferable to FFT convolution? Explain where overlap or discarded samples come from. Review FFT applications, implementation precision and block-processing exercises.
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.