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# dechirp

Perform dechirp operation on FMCW signal

## Description

example

y = dechirp(x,xref) mixes the incoming signal, x, with the reference signal, xref. The signals can be complex baseband signals. In an FMCW radar system, x is the received signal and xref is the transmitted signal.

## Examples

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### Dechirp FMCW Signal

Dechirp a delayed FMCW signal, and plot the spectrum before and after dechirping.

Create an FMCW signal.

```Fs = 2e5; Tm = 0.001;
hwav = phased.FMCWWaveform('SampleRate',Fs,'SweepTime',Tm);
xref = step(hwav);
```

Dechirp a delayed copy of the signal.

```x = [zeros(10,1); xref(1:end-10)];
y = dechirp(x,xref);
```

Plot the spectrum before dechirping.

```[Pxx,F] = periodogram(x,[],1024,Fs,'centered');
plot(F/1000,10*log10(Pxx)); grid;
xlabel('Frequency (kHz)');
ylabel('Power/Frequency (dB/Hz)');
title('Periodogram Power Spectral Density Estimate Before Dechirping');
```

Plot the spectrum after dechirping.

```[Pyy,F] = periodogram(y,[],1024,Fs,'centered');
plot(F/1000,10*log10(Pyy));
xlabel('Frequency (kHz)');
ylabel('Power/Frequency (dB/Hz)');
ylim([-100 -30]); grid
title('Periodogram Power Spectral Density Estimate After Dechirping');
```

## Input Arguments

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### x — Incoming signalM-by-N matrix

Incoming signal, specified as an M-by-N matrix. Each column of x is an independent signal and is individually mixed with xref.

Data Types: double
Complex Number Support: Yes

### xref — Reference signalM-by-1 vector

Reference signal, specified as an M-by-1 vector.

Data Types: double
Complex Number Support: Yes

## Output Arguments

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### y — Dechirped signalM-by-N matrix

Dechirped signal, returned as an M-by-N matrix. Each column is the mixer output for the corresponding column of x.

## More About

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### Algorithms

For column vectors x and xref, the mix operation is defined as xref .* conj(x).

If x has multiple columns, the mix operation applies the preceding expression to each column of x independently.

The mix operation negates the Doppler shift embedded in x, because of the order of xref and x.

The mixing order affects the sign of the imaginary part of y. There is no consistent convention in the literature about the mixing order. This function and the beat2range function use the same convention. If your program processes the output of dechirp in other ways, take the mixing order into account.

## References

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

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

## See Also

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