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Sampling converts an analog signal into a sequence of measured values taken at regular intervals. For a low-pass signal whose useful content extends from near DC to an upper frequency, the ideal minimum sampling rate is twice that upper frequency. But that Nyquist limit is not a complete design rule: unwanted frequencies can fold into the sampled band, so a filter before the ADC must control them. Wireless receivers can deliberately sample a filtered intermediate-frequency (IF) band below twice its carrier frequency, but only when the frequency plan and filtering prevent unwanted aliases.
What sampling does to a low-pass signal
An analog signal can vary continuously in time. An analog-to-digital converter (ADC) measures its input at discrete instants, set by the sampling rate, and represents those measurements as digital values. If the input is a low-pass signal, its wanted spectrum begins near DC and extends to a defined upper band edge.
Sampling does not simply preserve one copy of the input spectrum. In the frequency domain, sampling creates repeated copies, spaced at intervals equal to the sample rate. When those copies overlap, different analog frequencies can produce the same sampled pattern. Once that happens, the samples alone do not identify which frequency was originally present.
Nyquist limit: the minimum rate for the wanted band
For ideal reconstruction of a band-limited baseband signal with no content above a maximum frequency fmax, the theoretical minimum sample rate is 2 × fmax. The Nyquist frequency is half the sample rate; frequencies above it cannot be represented uniquely in the ordinary baseband interpretation.
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This is a lower bound under ideal assumptions, not a promise that sampling at exactly twice the signal’s upper edge will work in a real receiver. The input must be sufficiently band-limited, and the analog filter needs room to transition from passing wanted content to attenuating unwanted content.
A simple example
Suppose a wanted low-pass signal extends to 10 kHz. Its ideal Nyquist minimum is 20 kS/s. A 15 kHz unwanted tone, however, can fold to 5 kHz when sampled at 20 kS/s, because sampled data repeats every 20 kHz and the tone is 5 kHz below that repetition interval. The resulting 5 kHz component is indistinguishable by frequency alone from a genuine 5 kHz input tone.
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Aliasing: why out-of-band energy matters
Aliasing is frequency foldover caused by sampling. An unwanted input component can appear at a lower frequency in the digital data, potentially inside the wanted band. It is not a removable label attached to a sample: if an out-of-band tone aliases directly onto a wanted frequency, later digital processing cannot determine which source produced it.
A digital low-pass filter can remove digital frequencies that remain outside the retained band. It cannot reliably remove an unwanted analog component that has already folded into that band and become indistinguishable from wanted content. The prevention therefore has to begin before conversion.
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Why an anti-alias filter goes before the ADC
An analog anti-alias filter limits the frequencies reaching the sampler. In a baseband low-pass system, it passes the desired low-frequency band and attenuates higher frequencies that could alias into it. Its position is essential: filtering after the ADC is too late to separate overlapping aliases.
The filter is not expected to remove every trace of energy above a single sharp cutoff. Real filters roll off gradually rather than changing instantaneously from full pass to full rejection. Designers choose the wanted passband, sample rate, and stopband attenuation together so that the filter has enough frequency span to roll off before troublesome energy can alias into the band of interest.
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Why the practical rate is often higher than the minimum
National Instruments illustrates the transition-band issue with audio: for signal content up to 20 kHz, the ideal Nyquist minimum is 40 kHz, while practical sample-rate examples range from 44.1 kHz to 96 kHz. That is an audio illustration of margin for a real filter, not a universal sample-rate prescription for wireless systems. National Instruments explains anti-alias filters and their use.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How sampling applies to wireless IF receivers
A wireless receiver often selects a channel and translates it to an intermediate frequency before digital processing. In some designs, the wanted signal occupies a planned, band-limited IF range. The ADC can sample that band so it appears at a lower digital frequency, even though the IF center frequency is above the ADC’s Nyquist frequency. This is intentional undersampling, also called band-pass sampling.
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Undersampling is not arbitrary broadband RF sampling. The receiver has to plan where the wanted band maps after sampling and ensure other Nyquist zones do not produce overlapping aliases. The analog input filter must pass the wanted IF band while rejecting unwanted frequencies that would map into the same digital region. Digital filtering and mixing can then process the selected aliased band.
| Design consideration | Baseband low-pass sampling | IF undersampling |
|---|---|---|
| Wanted signal location | Near DC, extending to a defined upper band edge. | A selected, band-limited IF range at a planned center frequency. |
| Sampling and frequency mapping | Choose a rate at least twice the wanted upper frequency in the ideal case, with practical transition margin. | Plan the Nyquist-zone mapping so the wanted band lands in the intended digital region without overlapping unwanted images. |
| Analog filtering | A low-pass anti-alias filter attenuates higher-frequency input content. | A band-pass or resonant filter may be needed to select the IF band and reject other zones. |
| Key implementation concerns | Passband edge, stopband rejection, and sample-rate margin. | Filter response and impedance, insertion loss, ADC input-frequency capability, noise, distortion, and signal bandwidth. |
Analog Devices describes receiver designs in which IF placement, sampling rate, and filtering are coordinated so that unwanted harmonics or aliases fall outside the band of interest. The tradeoff is that some work shifts into frequency planning and filtering; undersampling does not remove the need to control unwanted input energy. Analog Devices discusses undersampling techniques for signal processing.
Why a high-IF filter may be specialized
A high-IF anti-alias filter is not necessarily a simple baseband low-pass network. Analog Devices application note AN-2542 describes a narrow-band resonant approach and explains that ADC and amplifier impedances affect the filter response. In practice, filter response, impedance, insertion loss, and converter performance must be considered as a connected design problem. Analog Devices AN-2542.
A measured example is not a general recipe
Analog Devices circuit note AN-2567 documents one receiver design with a 65 MHz-wide IF signal centered at 140 MHz and a 184.32 MSPS sampling rate. For that circuit, the note reports 70.1 dBFS SNR and 80.9 dBc SFDR at 140 MHz, and describes a fourth-order Butterworth anti-alias filter. These are results for that specific design, not general performance figures for wireless receivers or ADCs. Analog Devices AN-2567 circuit note.
Quick Recap
What to check when choosing a sampling approach
- Locate the wanted band. Establish whether the signal is baseband or a selected IF band, and define its actual bandwidth and edges.
- Map aliases before choosing the rate. Identify where the wanted band and plausible unwanted bands land in sampled frequency; verify that unwanted images do not overlap the wanted digital band.
- Design the analog filter around that map. Select a low-pass filter for a baseband case or an appropriate band-pass/resonant response for an IF case, with enough transition room and rejection.
- Check the converter and interface together. Confirm input-frequency capability and account for impedance, filter insertion loss, ADC drive, noise, distortion, and required bandwidth.
- Treat published circuit values as design-specific. A filter order, sampling rate, or measured performance in an application note describes that implementation; it is not a universal starting point or guarantee.
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