# dechirp

Perform dechirp operation on FMCW signal

## Syntax

• `y = dechirp(x,xref)` example

## 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`.

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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.