Digital Signal Processing Basics
Which of the following is a characteristic of an FIR (finite impulse response) filter?
- AIt has feedback from the output to the input side, so a steep response can be obtained with few coefficients
- BIts impulse response continues forever, so it easily becomes unstable when its coefficients are quantized
- CIt has no feedback, so it is always stable, and symmetric coefficients give it linear phase
Show answer and explanation
Answer: C. It has no feedback, so it is always stable, and symmetric coefficients give it linear phase
An FIR filter only multiplies the present and past inputs by coefficients and adds them; it has no output feedback. Its impulse response ends after the number of coefficients (taps), and its poles lie only at z = 0, so it is stable whatever the coefficient values. With symmetric coefficients it has linear phase, delaying every frequency component by the same time and preserving the shape of the waveform. In exchange, a steep response needs more taps than an IIR filter.
- A. Feedback and a steep response with few coefficients are characteristics of IIR filters.
- B. An infinitely long impulse response and possible instability from coefficient quantization belong to IIR filters.
- C. Correct. Without feedback it is stable, and symmetric coefficients give linear phase.