An ideal low-pass filter is characterized by which of the following?

An ideal low-pass filter is characterized by which of the following?

• A. A A constant gain with zero phase distortion in the pass band
• B. B A variable gain dependent on frequency
• C. C A sharp transition at high frequencies but undefined phase
• D. D A phase shift proportional to frequency (linear phase)

Answer: (A)

An ideal low-pass filter passes low-frequency components without changing their amplitude and preserves their relative timing, so the waveform in the passband stays intact. This is captured by having a constant gain in the passband along with zero phase distortion there. In other words, all frequencies the filter lets through are amplified equally and arrive with the same phase relationship, avoiding any reshaping of the signal.

If the gain varied with frequency, the waveform would be distorted because different frequencies would be amplified differently. If the phase were undefined or varied in a way that distorted relative timings, the waveform would again be warped. While linear phase is a desirable property, the essential description of an ideal low-pass in this context is the combination of flat passband gain and no phase distortion.