# range2beat

Convert range to beat frequency

## Syntax

• fb = range2beat(r,slope) example
• fb = range2beat(r,slope,c)

## Description

example

fb = range2beat(r,slope) converts the range of a dechirped linear FMCW signal to the corresponding beat frequency. slope is the slope of the FMCW sweep.

fb = range2beat(r,slope,c) specifies the signal propagation speed.

## Examples

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### Maximum Beat Frequency in FMCW Radar System

Calculate the maximum beat frequency in the received signal of an upsweep FMCW waveform. Assume that the waveform can detect a target as far as 18 km and sweeps a 300 MHz band in 1 ms. Also assume that the target is stationary.

slope = 300e6/1e-3;
r = 18e3;
fb = range2beat(r,slope);

## Input Arguments

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### r — Rangearray of nonnegative numbers

Range, specified as an array of nonnegative numbers in meters.

Data Types: double

### slope — Sweep slopenonzero scalar

Slope of FMCW sweep, specified as a nonzero scalar in hertz per second.

Data Types: double

### c — Signal propagation speedspeed of light (default) | positive scalar

Signal propagation speed, specified as a positive scalar in meters per second.

Data Types: double

## Output Arguments

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### fb — Beat frequency of dechirped signalarray of nonnegative numbers

Beat frequency of dechirped signal, returned as an array of nonnegative numbers in hertz. Each entry in fb is the beat frequency corresponding to the corresponding range in r. The dimensions of fb match the dimensions of r.

Data Types: double

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### Beat Frequency

For an up-sweep or down-sweep FMCW signal, the beat frequency is FtFr. In this expression, Ft is the transmitted signal's carrier frequency, and Fr is the received signal's carrier frequency.

For an FMCW signal with triangular sweep, the upsweep and downsweep have separate beat frequencies.

### Algorithms

The function computes 2*r*slope/c.

## References

[1] Pace, Phillip. Detecting and Classifying Low Probability of Intercept Radar. Artech House, Boston, 2009.

[2] Skolnik, M.I. Introduction to Radar Systems. New York: McGraw-Hill, 1980.