Can aliasing ever be used intentionally?

Yes. Undersampling (also called bandpass sampling or harmonic sampling) deliberately aliases a narrowband signal from a higher Nyquist zone into the first Nyquist zone, effectively performing frequency downconversion without a mixer. A 2.4 GHz signal with 20 MHz bandwidth can be sampled at 100 MSPS, placing it in the 48th Nyquist zone. The signal aliases down to a center frequency of either 0 to 50 MHz. This requires an extremely sharp bandpass filter before the ADC to reject all energy outside the desired band, and the ADC must have sufficient analog bandwidth (not just sample rate) to track the 2.4 GHz signal accurately.

Signal Processing

Aliasing

Q: How steep does the anti-aliasing filter need to be?

The filter must attenuate all energy above fs/2 to below the ADC's noise floor, typically 70 to 90 dB for a 12 to 16 bit converter. The transition band between the signal bandwidth and fs/2 determines the required filter order. For a 100 MSPS ADC digitizing a 40 MHz signal, the transition band is only 10 MHz (40 to 50 MHz) and 80 dB of rejection is needed, requiring a 7th-order or higher elliptic or Chebyshev filter. Using a higher sample rate widens the transition band and relaxes the filter requirement.

Q: Does clock jitter cause aliasing?

Not aliasing in the classical sense, but clock jitter has a similar effect: it spreads the signal spectrum and raises the noise floor. The SNR degradation from jitter is approximately SNR_jitter = -20 log10(2 pi f_signal t_jitter). At 1 GHz input with 100 fs RMS jitter, SNR_jitter = 64 dB, which limits a 14-bit ADC to about 10.3 effective bits regardless of its other specifications. This is why RF ADCs require ultra-low-jitter clock sources.

Sample a 60 MHz sine wave at 100 MSPS and you do not get a 60 MHz digital signal. You get a 40 MHz signal that is mathematically identical to the original at every sample point. The 60 MHz signal has folded around the 50 MHz Nyquist frequency and appeared as a phantom at 40 MHz, and no amount of digital processing can tell the difference. This is aliasing: any frequency component above half the sampling rate maps to a false lower frequency in the digitized output. The only defense is to remove those components before they reach the ADC, with an analog anti-aliasing filter.

Category: Signal Processing

Nyquist Criterion: f_s > 2f_max

Prevention: Anti-aliasing filter

Where the Missing Frequencies Reappear

Sampling at rate f_s creates periodic copies of the signal spectrum at multiples of f_s. The ADC output spectrum is the sum of all these copies. If the original signal has energy above f_s/2, copies overlap and add constructively, creating spectral content that was not in the original signal. Once folded in, aliased energy is indistinguishable from legitimate signal content.

Nyquist Zones and Spectral Folding

Nyquist zone definition (for sample rate f_s):
Zone 1: 0 to f_s/2
Zone 2: f_s/2 to f_s
Zone 3: f_s to 3f_s/2

Alias frequency formula:
f_alias = |f_signal − n·f_s| (choose n to place result in Zone 1)

Examples at f_s = 100 MSPS:
f = 30 MHz → f_alias = 30 MHz (Zone 1, no aliasing)
f = 60 MHz → f_alias = |60−100| = 40 MHz (folded from Zone 2)
f = 130 MHz → f_alias = |130−100| = 30 MHz (folded from Zone 3, overlaps Zone 1 signal)
f = 210 MHz → f_alias = |210−200| = 10 MHz (folded from Zone 5)

Anti-Aliasing Filter Requirements by ADC Resolution

ADC Bits	Dynamic Range	Required Filter Rejection	Typical Filter Order	Filter Type
8	48 dB	50 dB	3rd to 5th	Butterworth
12	72 dB	75 dB	5th to 7th	Chebyshev or elliptic
14	84 dB	85 dB	7th to 9th	Elliptic
16	96 dB	100 dB	9th to 11th	Elliptic or SAW

Common Questions

Frequently Asked Questions

Can aliasing be used intentionally?

Yes. Undersampling (bandpass sampling) deliberately aliases a narrowband signal from a higher Nyquist zone, effectively downconverting without a mixer. A 2.4 GHz signal can be sampled at 100 MSPS. This requires a sharp bandpass filter and sufficient ADC analog bandwidth to track the RF signal.

How steep does the anti-aliasing filter need to be?

It must attenuate above f_s/2 to below the ADC noise floor (70 to 90 dB for 12 to 16 bit). The transition band determines filter order. Oversampling widens the transition band and relaxes the filter.

Does clock jitter cause aliasing?

Not classical aliasing, but jitter spreads the spectrum and raises the noise floor. SNR_jitter = −20·log(2πf·t_j). At 1 GHz with 100 fs jitter, SNR is limited to 64 dB regardless of ADC specs.

Related Terms

← Aggregate Interference Ambiguity Function →

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