Sampling gordon lynchi introduction one of the aspects of research design often overlooked by researchers doing fieldwork in the study of religion is the issue of sampling. For functions that vary with time, let st be a continuous function or signal to be sampled, and let sampling be performed by measuring the value of the continuous function every t seconds, which is called the sampling interval or the sampling period. The shannonnyquist sampling theorem according to the shannonwhittaker sampling theorem, any square inte. Bandpass sampling can be utilized to downconvert a signal from rf or if to a. A bandpass sampling design in multichannel radio receiver core.
It is relatively commonplace for books and articles in the field particularly written from a humanities perspective to present their empirical data as being of self. Resulting conditions needed for aliasingfree bp sampling. The following examples illustrate how the sampling rates for bandpass signals may be selected. The required sampling frequency depends on the signal bandwidth, rather than on its highest frequency component. The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity. The ad9042 maintains 80 db spuriousfree dynamic range sfdr. Papoulis 1977 provided an elegant solution for the case where ft is a bandlimited function with finite energy and the sampling rate is equal to 2m times cutoff frequency. What were calling bandpass sampling goes by various other names in the literature, such as if sampling, harmonic sampling 2, subnyquist sampling, and under sampling 3. The main idea behind the bpsklike method is that the boc signal can be obtained as the sum of two bpsk signals, located at positive and negative subcarrier. Bandpass sampling can be utilized to downconvert a signal from rf or if to a bandpass signal at a lower if.
Web to pdf convert any web pages to highquality pdf. The theory of bandpass sampling signal processing, ieee transactions o n author. The sampling theorem and the bandpass theorem by d. Going back to the aliasing zone figure, if the signal of interest is in the zone other than zone 1, it is called a bandpass signal and the sampling operation is calledintermediate sampling or harmonic sampling or under sampling or bandpass sampling. Generalized sampling theorem for bandpass signals pdf. In the scheme, the bandpass sampling technique is introduced in rof systems to overcome the high sampling rate requirement and frontend hardware dependency of conventional digtal coherent receivers. The theory of bandpass sampling is presented in waters and jarrett, bandpass signal sampling and coherent detection, in ieee transactions on aerospace and electronic systems, vol.
The sampling theorem gives us a sufficient but not a necessary condition on the sampling frequency that we need to use with continuous time signal. Us20070140382a1 bandpass sampling receiver and the sampling. Potential sampling strategies has bandwidth b over hence b complex samples per second or 2b real samples per second samples each of and at a rate of b samples per second and reconstruction with complex bandpass interpolating function major problem with this is the design of practical analog of hilbert transformer for example. Learn more about signal processing signal processing toolbox. Handy online simulation tool models aliasing with lowpass and.
Bandpass sampling in heterodyne receivers for coherent optical access networks paraskevas bakopoulos, stefanos dris, bernhard schrenk, ioannis lazarou. If k is even the spectrum in the 0 to fs2 range is flipped. Lecture bandpass sampling by lyons 30 periodic sampling 2. Using the gsm 1800 signal as an example, the minimum sampling rate is only about. The theory of bandpass sampling signal processing, ieee.
In this case, undersampling or bandpass sampling techniques the analog. Osa bandpass sampling in heterodyne receivers for coherent. Bandpass sampling is a special form of undersampling that translates a high frequency bandpass signal to baseband frequency 4. The other alternative is the utilization of bandpass sampling. If a single adc is used, and b represents the occupied bandwidth of the signal of interest which differs from its maximum frequency, alias free reconstruction ofthe bandpass signal is not guaranteed for all sampling frequencies. Rouphael, in rf and digital signal processing for softwaredefined radio, 2009. Generalized bandpass sampling receivers for software. Sampling theorem bandpass or intermediate or under sampling. The minimum sampling frequency for a 2ghz bandpass signal with a bandwidth of 20 mhz is only about 40 mhz, as opposed to twice the highest frequency of 4 ghz. One way to accomplish this in a radio receiver front end is by direct downconverting the desired radio frequency rf signal to a target intermediate frequency if using bandpass sampling. For firstorder sampling, the acceptable and unacceptable sample rates. In this paper, the scope of the papoulis theory is extended to the case of bandpass signals.
In particular, the selection rule of bandpass sampling rate was. Bandpass sampling in heterodyne receivers for coherent. Handy online simulation tool models aliasing with lowpass and bandpass sampling rick lyons may 4, 2015 1 comment tweet analog devices inc. The range of acceptable uniform sampling rates is determined by. The minimum sampling rate required to avoid aliasing, as we have seen, is twice the onesided bandwidth of the modulated navigation. In bps, we can sample the signal at twice the information bandwidth and remain consistent with the nyquist sampling theorem. Bandpass sampling performs digitization and frequency translation in a single process.
There are a variety of techniques for sampling such signals, and these tech niques are generally referred to as bandpasssampling. Sampling theorem baseband sampling intermediate sampling or undersampling. The concept is targeted for wdm coherent optical access networks, where applying heterodyne. Use pdf download to do whatever you like with pdf files on the web and regain control. In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate below its nyquist rate twice the upper cutoff frequency, but is still able to reconstruct the signal. Direct downconversion of multiple rf signals using bandpass. Oct 25, 2016 can i get the code for bandpass sampling. Jun 17, 2019 sampling theorem mainly falls into two categories. The bandpass signal is repeated at integer multiples of the sampling frequency.
The lower graphs indicate how identical spectral results are created by the aliases of the sampling process. Consider the case where f h lb k an even integer k6 for this case whenever f h lb, we can choose fs 2b to perfectly interweave the shifted spectral replicas f l x f f. This page on low pass sampling vs band pass sampling describes basics of sampling of low pass signals and band pass signals and mention difference between these sampling techniques. The baseband function is sampled faster than its nyquist rate, and the bandpass function is undersampled, effectively converting it to baseband. Bandpass sampling is a special form of undersampling that translates a high frequency. In bandpass sampling, were more concerned with a signals bandwidth than its highest frequency component. Bandpass sampling an overview sciencedirect topics. Generalized sampling theorem for bandpass signals eurasip. A bandpass sampling based digital coherent receiver is presented for phase modulated radiooverfiber links with coherent detection. Bandpass sampling for software radio receivers, and the effect of oversampling on aperture jitter. By analog bandpass signal we mean an analog signal having the spectrum shown in figure 1a with its spectral energy centered at f c hz. In signal processing, undersampling or bandpass sampling is a technique where one samples. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal.
Bandpass sampling of qpsk in systemvue bandpass s ampling of a qpsk signal can be demonstrated with the systemvue model shown in figure 1. Bandwidth is simply the difference between the lowest and the highest frequency present in the signal. It demonstrates the application of bandpass sampling in an optical communications context, to overcome the high sampling rate requirement of conventional receivers more than twice the signal bandwidth. Bandpass sampling in highorder boc signal acquisition. Hindawi publishing corporation eurasip journal on applied signal processing volume 2006 generalized sampling theorem for bandpass signals 0 department of radio electronics, brno university of technology, purkynova 118, 612 00 brno, czech republic the reconstruction of an unknown continuously defined function f t from the samples of the responses of m linear timeinvariant lti systems. View notes lecture bandpass sampling by lyons from ee 6360 at university of texas, dallas. Bandpass sampling methodology for uniformly spaced. The sampling frame is the list of ultimate sampling entities, which may be people, households, organizations, or other units of analysis. Bandpass sampling based digital coherent receiver with free. According to the bandpass sampling theory 5, the minimum sampling rate is dependent on the bandwidth, but not the maximum frequency, of the rf signal. Oct 31, 20 bandpass sampling in bandpass sampling also called undersampling, we apply an analog bandpass signal to an ad converter and obtain a digitized timedomain sequence representing that analog signal.
Computing translated frequencies in digitizing and. Rearrange individual pages or entire files in the desired order. A novel digital receiver architecture for coherent heterodynedetected optical signals is presented. This is not usually a problem since the next step after bp sampling is usually to create the lowpass equivalent signal, which can be done in a way that gives either spectral orientation. The condition for a nondestructive sample rate is that the aliases of both bands do not overlap when. In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpassfiltered signal at a sample rate below its nyquist rate twice the upper cutoff frequency, but is still able to reconstruct the signal when one undersamples a bandpass signal, the samples are indistinguishable from the samples of a lowfrequency alias of the highfrequency signal.