"Estimation of the Degree of Signal Sparseness for the Application of Compressed Sampling Theory to Frequency-Sparse Signals"

"The application of compressed sampling theory for processing frequency-sparse signals is of considerable interest in the field of digital signal processing. An approach based on the use of a random demodulator architecture is known, which allows applying the compressed sampling theory to significantly reduce the requirement for analog-to-digital conversion under the condition of sparseness of the processed signal. This paper presents the results of a study that defines the conditions for an acceptable degree of signal sparseness for the effective application of compressed sampling theory. Using a signal with typical parameters as an example, it is shown that the sampling frequency can be significantly reduced without loss of information. Based on mathematical modeling, a practical method for calculating the degree of sparseness is proposed. Thus, the work demonstrates that the application of compressed sampling theory based on a random demodulator in data acquisition systems allows optimizing the sampling process, but requires determining the required degree of sparseness of the input signal."