What is the output equation for a causal order-$N$ FIR filter?

$y[n]=\sum_{i=0}^{N} b_i x[n-i]$, a weighted sum of the current and delayed input samples.

Why is a finite-coefficient FIR filter BIBO stable?

For bounded input, its output is bounded by the input bound times the finite sum of the absolute coefficient values.

How can an FIR filter be designed for linear phase?

Use a symmetric or, in applicable designs, antisymmetric coefficient sequence.

What is the frequency response of a causal FIR filter?

For coefficients $b_0$ through $b_N$, it is $H(e^{j\omega})=\sum_{n=0}^{N}b_n e^{-j\omega n}$.

What does the window method do in FIR design?

It truncates an ideal impulse response by multiplying it by a finite window.

Signal processingLesson 1 of 1 in the course Digital filters

FIR Filters: Models, Frequency Response, Properties, and Design

5 flashcards · 5 quiz questions · 5 match pairs · 3 fill-in sentences · English

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Summary

A finite impulse response (FIR) filter produces an output whose response to an impulse lasts for a finite number of samples. This lesson introduces the FIR model and shows how input samples, coefficients, and delayed samples combine to form an output.

An FIR filter has an impulse response that becomes zero after a finite duration. For a causal, discrete-time FIR filter of order $N$ , the impulse response occupies at most $N+1$ sample positions, from $n=0$ through $n=N$ .

All flashcards

What is the output equation for a causal order- $N$ FIR filter?: $y[n]=\sum_{i=0}^{N} b_i x[n-i]$ , a weighted sum of the current and delayed input samples.
Why is a finite-coefficient FIR filter BIBO stable?: For bounded input, its output is bounded by the input bound times the finite sum of the absolute coefficient values.
How can an FIR filter be designed for linear phase?: Use a symmetric or, in applicable designs, antisymmetric coefficient sequence.
What is the frequency response of a causal FIR filter?: For coefficients $b_0$ through $b_N$ , it is $H(e^{j\omega})=\sum_{n=0}^{N}b_n e^{-j\omega n}$ .
What does the window method do in FIR design?: It truncates an ideal impulse response by multiplying it by a finite window.

Quiz questions

What error criterion does the Parks–McClellan method minimize?Answer: Maximum weighted deviation from the desired response.
How are the coefficients of a matched filter for a known pulse shape obtained?Answer: Use samples of the known pulse shape in reverse order.
What is the Nyquist frequency in normalized angular frequency?Answer: $\pi$ radians per sample.
For a causal FIR filter, how can its frequency response be expressed using its coefficients?Answer: $H(e^{j\omega})=\sum_{n=0}^{N}b_n e^{-j\omega n}$ .
What phase property can a symmetric FIR coefficient sequence be designed to produce?Answer: Linear phase across frequency.

Based on the Wikipedia article Finite impulse response, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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