**6. Acknowledgment**

166 Applications of Digital Signal Processing

R. 1118 - S. 1 2278 2265 4 13 0,5% R. 118 - S. 2 2278 2263 11 15 1,80% R. 108 – S. 1 562 538 35 24 10,49% R. 108 – S. 2 562 524 76 38 20,28% Table 6. Results obtained with the Holsinger Algorithm Modified Version 2, for some of the

R. 1118 - S. 1 2278 2265 1 1 0,08% R. 118 - S. 2 2278 2263 1 2 0,13% R. 108 – S. 1 562 542 1 15 2,84% R. 108 – S. 2 562 538 23 21 7,82% Table 7. Results obtained with the Holsinger Algorithm Modified Version 3, for some of the

The implementation of equipments for the acquisition and processing of bioelectrical human signals such as the ECG signal is currently a viable task. This chapter is a summary of previous works with simple equipment to work with the ECG signal. Currently the authors

x Increase the number of leads purchased. The A/D converter allows up to 11 simultaneous inputs and supports a sampling rate of 32 KHz. Under certain conditions.

x Modify RC filters in the filter stage for more elaborate filters to ensure a better

x Include isolation amplifiers to increase levels for the security of patients, isolating the direct loop with the computer, which is generated with the design proposed in this chapter. Even with the probability of a catastrophe to occur which are low, but the possibility exists and such massive use should be avoided, before including these

x Certify the technical characteristics of the circuits mounted in order to validate its

x Increase the use of this equipment for capturing other bioelectrical signals such as

x Implement a tool to validate algorithms of detection QRS, based on the MIT DB.

12 simultaneous leads are required for a professional team.

discrimination of the frequencies that are outside the pass-band.

x Unifying routine readings of A/D converter and display of results.

electroencephalographic and electromygraphic.

**False Positives (PF)** 

**False Positives (PF)** 

**False Negatives (NF)** 

**False Negatives (NF)** 

**(PF + NF) / NL** 

**(PF + NF) / NL** 

**True Positives (PV)** 

**True Positives (PV)** 

**Signal** 

**Signal** 

MIT Database records

MIT Database records

**5. Conclusion** 

are working on:

amplifiers.

massive use.

**Future works:** 

x Improvements to the work done:

**Pulses Heart (NL)** 

**Pulses Heart (NL)** 

To Dr. David Cuesta of the Universidad Politécnica de Valencia for his valuable contributions and excellent disposition to the authors of this work; to cardiologist Dr. Patricio Maragaño, director of the Regional Hospital of Talca's Cardiology department, for his clinical assessment and technical recommendations for the development of the algorithmic procedures undertaken.

### **7. References**


**9** 

**Applications of the Orthogonal Matching** 

**to Compressive Sensing Recovery** 

George C. Valley and T. Justin Shaw

*The Aerospace Corporation* 

*United States* 

**Pursuit/ Nonlinear Least Squares Algorithm** 

Compressive sensing (CS) has been widely investigated as a method to reduce the sampling rate needed to obtain accurate measurements of sparse signals (Donoho, 2006; Candes & Tao, 2006; Baraniuk, 2007; Candes & Wakin, 2008; Loris, 2008; Candes et al., 2011; Duarte & Baraniuk, 2011). CS depends on mixing a sparse input signal (or image) down in dimension, digitizing the reduced dimension signal, and recovering the input signal through optimization algorithms. Two classes of recovery algorithms have been extensively used. One class is based on finding the sparse target vector with the minimum ell-1 norm that satisfies the measurement constraint: that is, when the vector is transformed back to the input signal domain and multiplied by the mixing matrix, it satisfies the reduced dimension measurement. In the presence of noise, recovery proceeds by minimizing the ell-1 norm plus a term proportional to ell-2 norm of the measurement constraint (Candes and Wakin, 2008; Loris, 2008). The second class is based on "greedy" algorithms such as orthogonal matching pursuit (Tropp and Gilbert, 2007) and iteratively, finds and removes elements of a discrete

There is, however, a difficulty in applying these algorithms to CS recovery for a signal that consists of a few sinusoids of arbitrary frequency (Duarte & Baraniuk, 2010). The standard discrete Fourier transform (DFT), which one expects to sparsify a time series for the input signal, yields a sparse result only if the duration of the time series is an integer number of periods of each of the sinusoids. If there are *N* time steps in the time window, there are just *N* frequencies that are sparse under the DFT; we will refer to these frequencies as being on the frequency grid for the DFT just as the time samples are on the time grid. To recover signals that consist of frequencies off the grid, there are several alternative approaches: 1) decreasing the grid spacing so that more signal frequencies are on the grid by using an overcomplete dictionary, 2) windowing or apodization to improve sparsity by reducing the size of the sidelobes in the DFT of a time series for a frequency off the grid, and 3) scanning the DFT off integer values to find the frequency (Shaw & Valley, 2010). However, none of these approaches is really practical for obtaining high precision values of the frequency and amplitude of arbitrary sinusoids. As shown below in Section 6, calculations with time windows of more than 10,000 time samples become prohibatively slow; windowing distorts the signal and in many cases, does not improve sparsity enough for CS recovery algorithms

dictionary that are maximally correlated with the measurement.

**1. Introduction** 

