Chapter 8 analogtodigital and digital to analog conversion. But in case of bandpass signal, undersampling sampling rate less than nyquist rate can also do the job. Ee4512 analog and digital communications chapter 8 a bandpass signal does not need to be sampled at 2 f 2. We can always use nyquist theorem to decide the sampling rate. Bandpass sampling an overview sciencedirect topics. 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. The classical bandpass theorem for uniform sampling states that the signal can be reconstructed if the sampling rate is at least f min 2fxn, where n is the largest.
The theory of bandpass sampling signal processing, ieee. In the first part, a generalized sampling theorem gst for bandpass signals is presented. Sampling theorem baseband sampling intermediate sampling or under sampling. Here the effective sampling rate is also 4 w samplessec.
The main advantage of this is, therefore, the reduced requirement of the sampling frequency and of the. In this paper, the scope of the papoulis theory is extended to the case of bandpass signals. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal. In the analysis and actual processing of bp signals it is convenient to work with a related, equivalent signal called the. Sampling theorem bandpass or intermediate or under. Thus, the bandpass signal can be perfectly reconstructed from two interleaved uniformly sampled sequences using the above interpolation. A bandpass sampling design in multichannel radio receiver core.
There are so many different time and frequencydomain methods for generating complex baseband and analytic bandpass signals that i had trouble keeping those techniques straight in my mind. Sampling theorem for band pass signals topics discussed. Q3 when it comes to baseband sampling low pass sampling sampling theorem states that fs twice the highest frequency component and for bandpass sampling, sampling theorem says fs twice the bandwidth of the signal. The required sampling frequency depends on the signal bandwidth, rather than on its highest frequency component.
Rouphael, in rf and digital signal processing for softwaredefined radio, 2009. If k is even the spectrum in the 0 to fs2 range is flipped. Sampling subsystem analog 16000hz because there construction is performed with the lowest frequency possible. A feedback signal which is synthesized from these four signals is sampled by the fifth adcs. Sampling subsystem analog sampling rate lower than twice the highest frequency could be used. We use the fourier transform to understand the discrete sampling and resampling of signals. The sampling theorem shows that a bandlimited continuous signal can be perfectly reconstructed from a sequence of samples if the highest frequency of the. Periodically nonuniform sampling of bandpass signals. We can use a technique known as bandpass sampling to sample a continuous bandpass signal that is centered about some frequency other than zero hz. Pdf the reconstruction of an unknown continuously defined function ft from the samples of the responses of m linear timeinvariant lti.
One key question is when does sampling or resampling provide an adequate representation of the original signal. When a continuous input signal s bandwidth and center. A continuous time signal can be represented in its samples and can be recovered back when sampling frequency f s is greater than or equal to the twice the highest frequency component of message signal. Pdf generalized sampling theorem for bandpass signals.
In the statement of the theorem, the sampling interval has been taken as. Sampling bandpass signals understanding digital signal. The sampling theorem and the bandpass theorem by d. Sampling theorem baseband sampling intermediate sampling or undersampling. 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. Generating complex baseband and analytic bandpass signals. The bandpass signal is repeated at integer multiples of the sampling frequency. The sampling theorem shows that a bandlimited continuous signal can be perfectly reconstructed from a sequence of samples if the highest frequency of the signal does not exceed half the rate of sampling. Although satisfying the majority of sampling requirements, the sampling of lowpass signals, as in figure 26, is not the only sampling scheme used in practice. The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity. The shannonnyquist sampling theorem according to the shannonwhittaker sampling theorem, any square inte. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions. It is perceivable that the complexity of firstorder sampling of bandpass signals increases dramatically if the signal has multiple passbands, unless the signal is treated as a lowpass signal or a singleband bandpass signal.
479 400 1623 183 553 1600 591 730 477 401 368 443 29 661 913 1600 796 115 1258 701 65 1352 517 918 246 1119 444 648 1427 1104 448 1061