Digital Filters: Models, Realizations, and Design Trade-Offs

All flashcards

Transfer function

A mathematical representation that characterizes a linear, time-invariant filter, often as a ratio of polynomials in the Z-domain.

Impulse response

The output sequence produced by a filter when its input is a discrete-time impulse.

Filter realization

A signal-flow structure or algorithm that implements a filter’s transfer function.

Direct form II

A filter realization that combines delay elements to reduce storage requirements compared with direct form I.

State-space model

A system description that represents behavior using internal state variables.

Quiz questions

1. For a transfer function with numerator order $N$ and denominator order $M$, how is filter order defined?Answer: As the greater of $N$ and $M$.
2. Which property defines a finite impulse response (FIR) filter?Answer: Its impulse response becomes zero after a finite number of samples.
3. What is a typical benefit and trade-off of direct form II?Answer: It uses fewer delay elements but can increase overflow risk in resonant filters.
4. What condition makes a filter linear?Answer: It satisfies superposition: weighted input combinations produce the same weighted output combinations.
5. How does an FFT-based filtering approach typically process a signal?Answer: It transforms the signal to the frequency domain, modifies its spectrum, then applies an inverse FFT.