# Documentation

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# dop2speed

Convert Doppler shift to speed

## Syntax

```radvel = dop2speed(Doppler_shift,wavelength) ```

## Description

`radvel = dop2speed(Doppler_shift,wavelength)` returns the radial velocity in meters per second. This value corresponds to the one-way Doppler shift, `Doppler_shift`, for the wavelength, `wavelength`, in meters.

## Examples

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Calculate the radial velocity of an automobile based on the Doppler shift of a continuous-wave radar. The radar carrier frequency is 24.15 GHz. Assume a doppler shift of 2.880 kHz.

```f0 = 24.15e9; lambda = physconst('LightSpeed')/f0; dopshift = 2.880e3; radvel = dop2speed(dopshift,lambda)```
```radvel = 35.7516 ```

The radial velocity is approximately 35.75 meters per second or 80 miles/hour.

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The radial velocity of a source relative to a receiver can be computed from the one-way Doppler shift:

`${V}_{s,r}=\Delta f\lambda$`
where Vs,r denotes the radial velocity of the source relative to the receiver, Δf is the Doppler shift in hertz, and λ is the carrier frequency wavelength in meters.

## References

[1] Rappaport, T. Wireless Communications: Principles & Practices. Upper Saddle River, NJ: Prentice Hall, 1996.

[2] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.