Abstract: Given a large sparse signal, great wishes are to
reconstruct the signal precisely and accurately from lease number of
measurements as possible as it could. Although this seems possible
by theory, the difficulty is in built an algorithm to perform the
accuracy and efficiency of reconstructing. This paper proposes a new
proved method to reconstruct sparse signal depend on using new
method called Least Support Matching Pursuit (LS-OMP) merge it
with the theory of Partial Knowing Support (PSK) given new method
called Partially Knowing of Least Support Orthogonal Matching
Pursuit (PKLS-OMP).
The new methods depend on the greedy algorithm to compute the
support which depends on the number of iterations. So to make it
faster, the PKLS-OMP adds the idea of partial knowing support of its
algorithm. It shows the efficiency, simplicity, and accuracy to get
back the original signal if the sampling matrix satisfies the Restricted
Isometry Property (RIP).
Simulation results also show that it outperforms many algorithms
especially for compressible signals.
Abstract: The paper deals with the estimation of amplitude and phase of an analogue multi-harmonic band-limited signal from irregularly spaced sampling values. To this end, assuming the signal fundamental frequency is known in advance (i.e., estimated at an independent stage), a complexity-reduced algorithm for signal reconstruction in time domain is proposed. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. The proposed algorithm for the calculation of the unknown parameters requires O((2M+1)2) flops, while the straightforward solution of the obtained equations takes O((2M+1)3) flops (M is the number of the harmonic components). It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise RMS measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.