The Sampling Theorem of Signal Processing

Author(s):  
Paul L. Butzer
2021 ◽  
Vol 1 (6) ◽  
pp. 6-11
Author(s):  
Nyein Mynt ◽  
Zaw Aung ◽  
Kyaw Lin

This practicum is to define the study properties of the sampling theorem. Understand the effect of selecting the sample size and its effect on the signal recovery process. The experiment utilizes a computer or portable workstation to run an examination of the hypothesis reenactment program. From the test information gotten, it can be concluded that the more noteworthy the frequency of the signal to be inspected, the closer the signal will be to the initial signal. The time and frequency of the examining signal are conversely relative. The higher the frequency, the lower the time will be. The magnitude of the amplitude of the output signal is indeterminate.


2014 ◽  
Vol 926-930 ◽  
pp. 2992-2995
Author(s):  
Zheng Pu Zhang ◽  
Xing Feng Guo ◽  
Bo Tian

Compressive sensing is a new type of digital signal processing method. The novel objective of compressive Sensing is to reconstruct a signal accurately and efficiently from far fewer sampling points got by Nyquist sampling theorem. Compressive sensing theory combines the process of sampling and compression to reduce the complexity of signal processing, which is widely used in many fields. so there are wide application prospects in the areas of radar image, wireless sensor network (WSN), radio frequency communication, medical image processing, image device collecting and so on. One of the important tasks in CS is how to recover the signals more accurately and effectively, which is concerned by many researchers. Compressive sensing started late; there are many problems and research directions worthy of our in-depth research. At present, many researchers shove focused on reconstruction algorithms. Reconstruction algorithms are the core of compressive sensing, which are of great significance to reconstructing compressed signals and verifying the accuracy in sampling. These papers introduce CosaMP algorithm; and then study and analyze the Gaussian noise as the main content. Finally, the given signal and random signal, for example, we give a series of comparison results.


2011 ◽  
Vol 282-283 ◽  
pp. 437-439
Author(s):  
Lan Feng Wang ◽  
Kai Jun Sun ◽  
Jing Ben Yin

Sampling theorem plays an important role in many fields such as signal processing and image processing. In this paper, the cardinal orthogonal scaling function with dilation factor 3 is classified by the highpass filter coefficient, thus, the sampling theorem in the wavelet subspace is obtained. Then, the symmetry property of cardinal orthogonal scaling function is discussed.


Author(s):  
Guojun Qin ◽  
Jingfang Wang

<p>The classical Shannon/Nyquist sampling theorem tells us that in order to not lose information when uniformly sampling a signal we must sample at least two times faster than its bandwidth. Nowadays in many applications, because of the restriction of the Nyquist rate, we end up with too many samples and it becomes a great challenge for further transmission and storage. In recent years, an emerging theory of signal acquirement, compressed sensing(CS), is a ground-breaking idea compared with the conventional framework of Nyquist sampling theorem. It considers the sampling in an novel way, and open up a brand new field for signal sampling process. It also reveals a promising future of application. In this paper, we review the background of compressed sensing development. We introduce the framework of CS and the key technique and illustrate some naïve application on image process.</p>


2013 ◽  
Vol 275-277 ◽  
pp. 2523-2526
Author(s):  
Xin Cheng Zhang

Sampling theorem plays an important role in the engineering such as signal processing, image processing, digital communications, and so on. In this paper, the symmetry property of cardinal orthogonal scaling function is discussed. Then, a 4-band cardinal orthogonal scaling function from the relation between the highpass filter coefficients and wavelet is provided. Thus, sampling theorem in the wavelet subspace is obtained.


2013 ◽  
Vol 709 ◽  
pp. 563-566
Author(s):  
Jin Zhou Li ◽  
Xin Cheng Zhang

Sampling theorem has a key role in signal processing and image processing. In this paper, the scaling functions with cardinal property are discussed in the dimensions and their symmetry property is classified. Therefore, sampling theorems of wavelet subspaces are obtained. Then, the cardinal orthogonal scaling function with cardinal property is characterized in the dimensions and an equation between the highpass filter coefficients and wavelet samples are got. The existing results are generalized to the case of M band.


Author(s):  
Jean-Luc Starck ◽  
Fionn Murtagh ◽  
Jalal Fadili
Keyword(s):  

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