An ideal low-pass filter has a constant amplitude and linear phase in the passband. Why is linear phase desirable?

An ideal low-pass filter has a constant amplitude and linear phase in the passband. Why is linear phase desirable?

• A. Preserves waveform shapes in the passband
• B. Increases bandwidth
• C. Reduces quantization noise
• D. Introduces extra delay

Answer: (A)

Linear phase means the phase shift across frequencies is proportional to frequency, which gives a constant group delay. In an ideal low-pass with a flat passband magnitude, this means every frequency component in the passband is delayed by the same amount. Because all components experience the same delay, their relative timing stays the same, so the overall time-domain waveform shape is preserved—even for short transients or sharp pulses. The signal is simply shifted in time without distortion, which is exactly why linear phase is desirable.

The other points don’t address this waveform-preserving property. Linear phase does introduce a fixed delay, but that does not distort the shape; it just moves the signal in time. Bandwidth, quantization noise, or that delay in isolation don’t capture the benefit of keeping the waveform intact.