Bandpass Sampling for Direct Downconversion

Sampling at rates lower than 2f

 still can allow for an exact reconstruction of the information 

content of the analog signal if the signal is a bandpass signal. An ideal bandpass signal has no 

frequency components below a certain frequency f

 and above a certain frequency f

. Typically, 

bandpass signals have f

l

 » f

 - f

. For a bandpass signal, the minimum requirement on the 

sampling rate to allow for exact reconstruction is that the sampling rate be at least two times the 

bandwidth f

 - f

 of the signal.  

Sampling at a rate two times the bandwidth of a signal is called the Nyquist sampling rate. When 

the signal is a baseband signal (a signal with frequency content from DC to f

) the Nyquist 

sampling rate is 2f

max

. For bandpass signals, however, the Nyquist sampling rate is 2(f

 - f

). To 

bandwidth of the bandpass signal and two times the highest frequency in the bandpass signal, the 

sampling frequency f

s

 must satisfy [4]  

  is restricted to integer values that satisfy        

. 

These equations show that only certain ranges of sampling rates can be used if spectrum overlap 

Bandpass sampling can be used to downconvert a signal from a bandpass signal at an RF or IF to 

a bandpass signal at a lower IF. Since the bandpass signal is repeated at integer multiples of the 

sampling frequency, selecting the appropriate spectral replica of the original bandpass signal 

provides the downconversion function.  

Bandpass sampling holds promise for radio receivers that digitize directly at the RF or IF since 

the desired input signals to radio receivers are normally bandpass signals. Theoretically, 

bandpass sampling allows sampling rates to be much lower than those required by sampling at 

two or more times the highest frequency content of the bandpass signal. This implies that ADCs 

with slower sampling rates (and therefore potentially higher performance, lower power 

consumption, or lower cost) may be used. An important practical limitation, when using 

bandpass sampling, is that the ADC must still be able to effectively operate on the highest 

 

8 

frequency component in the signal. This specification is usually given as the analog input 

bandwidth for the ADC.  

Conventional ADCs are designed to operate on signals with maximum frequencies up to one-half 

the sampling rate. In other words, conventional ADCs typically are not suitable for bandpass 

sampling applications where the maximum input frequencies are greater than the sampling rate. 

Furthermore, for conventional ADCs, many manufacturers provide specifications only at 

frequencies well below one-half the maximum sampling rate. In general, performance of ADCs 

typically degrades with increased input frequency. Therefore, in using ADCs for frequencies 

near one-half the maximum sampling rate or for bandpass sampling applications, the 

specifications of the converter must be determined and carefully examined at the desired input 

frequencies. In addition, when bandpass sampling, stringent requirements on analog bandpass 

filters (steep rolloffs) are needed to prevent distortion of the desired signal from strong adjacent 

channel signals.  

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