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Convert range to beat frequency



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.


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Calculate the maximum beat frequency in MHz for an upsweep FMCW waveform. The waveform sweeps a 300 MHz band in 1 ms. Assume that the waveform can detect a stationary target as far as 18 km.

slope = 300e6/1e-3;
r = 18e3;
fb = range2beat(r,slope)/1e6
fb = 36.0249

Input Arguments

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

Data Types: double

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

Data Types: double

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

Data Types: double

Output Arguments

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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

More About

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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.


The function computes 2*r*slope/c.


[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.

Extended Capabilities

Version History

Introduced in R2012b