エイリアシング

Aliasing occurs when the sampling frequency falls below the Nyquist rate, causing spectral replicas of the original signal to overlap in the frequency domain. This overlapping prevents accurate recovery of the original signal using a low-pass filter, resulting in a distorted reconstructed signal that cannot return to its original form.

The Nyquist rate, which equals twice the highest frequency in the original signal, ensures the sampling frequency is high enough to capture necessary signal information. When sampling exceeds this rate, spectral replicas do not overlap, allowing accurate reconstruction of the original signal and avoiding aliasing distortion.

When the fundamental frequency lies between half the sampling frequency and the sampling frequency itself, aliasing creates a counterintuitive effect where higher frequencies become indistinguishable from lower frequencies. This causes the perceived output frequency to decrease as the fundamental frequency increases, a direct result of spectral replica overlap.

Sampling a signal at a specific frequency creates multiple scaled replicas of the original spectrum in the frequency domain. The spacing between these replicas is determined by the sampling frequency. If the sampling frequency is too low, these replicas overlap, causing aliasing and signal distortion.

Accurate signal recovery requires the sampling frequency to exceed the Nyquist rate, preventing spectral replica overlap. Once this condition is met, a low-pass filter can extract the original signal spectrum. Reconstruction of signal using interpolation techniques further enables faithful recovery of the original time-domain signal.

The spacing of spectral replicas in the frequency domain is directly determined by the sampling frequency. Higher sampling frequencies create wider spacing between replicas, reducing overlap risk. Lower sampling frequencies compress replica spacing, increasing the likelihood of overlap and aliasing when the sampling frequency drops below the Nyquist rate.

When the fundamental frequency is less than half the sampling frequency, increasing the fundamental frequency produces an expected increase in output frequency. This predictable behavior allows clearer signal reconstruction and occurs because spectral replicas remain separated, avoiding aliasing effects that would distort the output.