# pulsint

Pulse integration

## Syntax

Y = pulsint(X)
Y = pulsint(X,METHOD)

## Description

Y = pulsint(X) performs video (noncoherent) integration of the pulses in X and returns the integrated output in Y. Each column of X is one pulse.

Y = pulsint(X,METHOD) performs pulse integration using the specified method. METHOD is 'coherent' or 'noncoherent'.

## Input Arguments

 X Pulse input data. Each column of X is one pulse. METHOD Pulse integration method. METHOD is the method used to integrate the pulses in the columns of X. Valid values of METHOD are 'coherent' and 'noncoherent'. The values are not case sensitive. Default: 'noncoherent'

## Output Arguments

 Y Integrated pulse. Y is an N-by-1 column vector where N is the number of rows in the input X.

## Examples

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Noncoherently integrate 10 pulses of a sinusoid with added gaussian white noise.

npulse = 10;
x = repmat(sin(2*pi*(0:99)'/100),1,npulse) + 0.1*randn(100,npulse);
y = pulsint(x);

Plot a single pulse and then the integrated pulses.

subplot(2,1,1)
plot(abs(x(:,1)))
ylabel('Magnitude')
title('First Pulse')
subplot(2,1,2)
plot(abs(y))
ylabel('Magnitude')
title('Integrated Pulse')

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### Coherent Integration

Let Xij denote the (i,j)-th entry of an M-by-N matrix of pulses X.

The coherent integration of the pulses in X is:

${Y}_{i}=\sum _{j=1}^{N}{X}_{ij}$

### Noncoherent (video) Integration

Let Xij denote the (i,j)-th entry of an M-by-N matrix of pulses X.

The noncoherent (video) integration of the pulses in X is:

${Y}_{i}=\sqrt{\sum _{j=1}^{N}|{X}_{ij}{|}^{2}}$

## References

[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.