# Determine the delay between two signals
**URL:** https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140
**Category:** Signal and Image Processing
**Tags:** question
**Created:** [January 23, 2024, 1:52pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140 "2024-01-23T13:52:38Z")
**Posts on this page:** 13
**Page:** 1
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [January 23, 2024, 1:52pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/1 "2024-01-23T13:52:38Z")
Hello,
I am trying to find out the delay between two signals. I have the following Python example:
```julia
# Cross-correlate
correlation = correlate(x, y, 'full')
# Get the lag vector that corresponds to the correlation vector
lags = correlation_lags(x.size, y.size, mode="full")
# Find the lag at the peak of the correlation
lag = lags[np.argmax(correlation)]
print(lag)
```
My Julia code so far:
```julia
using StatsBase
function delay(x, y)
z = crosscor(x, y)
ind = argmax(z)
end
```
But there is still something like the Python function `correlation_lags` missing, see: [scipy.signal.correlation\_lags — SciPy v1.12.0 Manual](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.correlation_lags.html)
If I call my delay function with the same vector for both arguments I get a result that is not zero, but the delay in this test case should be zero.
Any idea?
---
### Author:  [@Jake](https://discourse.julialang.org/u/Jake)
#### Post date: [January 23, 2024, 2:10pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/2 "2024-01-23T14:10:44Z")
Try [DSP.xcorr.](https://docs.juliadsp.org/stable/convolutions/)
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [January 23, 2024, 2:19pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/3 "2024-01-23T14:19:30Z")
Different result, but not better. I want to get the delay between the two signals in time-steps.
---
### Author:  [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)
#### Post date: [January 23, 2024, 2:28pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/4 "2024-01-23T14:28:10Z")
```julia
crosscor(x, y)
When left unspecified, the lags used are the integers from `-min(size(x,1)-1, 10*log10(size(x,1)))` to `min(size(x,1), 10*log10(size(x,1)))`
```
so it means zero lag is in the middle of z if you use delay with the same vector for both arguments.
---
### Author:  [@mgkuhn](https://discourse.julialang.org/u/mgkuhn)
#### Post date: [January 23, 2024, 2:36pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/5 "2024-01-23T14:36:55Z")
There probably ought to be a variant of `DSP.xcorr` that returns an `OffsetArray`, such that the indices are lags. And that should ideally also work correctly if any of the inputs is `OffsetArray`. Also a `maxlag` option to truncate the output would be nice.
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [January 23, 2024, 2:39pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/6 "2024-01-23T14:39:43Z")
```julia
using StatsBase
T=0:0.1:10
X=sin.(T)
Y=sin.(T.-0.5)
plot(T,X)
plot(T,Y)
z = StatsBase.crosscor(X, Y)
delay=argmax(z)
println(delay)
```
This prints a delay of 26, but the expected delay is 0.5s = 5 time steps. How can I get the correct result?
---
### Author:  [@mgkuhn](https://discourse.julialang.org/u/mgkuhn)
#### Post date: [January 23, 2024, 2:46pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/7 "2024-01-23T14:46:28Z")
In your case, the answer should probably be:
```julia
delay=argmax(z) - length(T)
```
It is more tricky if `length(X) != length(Y)`, as then there is the question what the zero alignment between the two sequences should be (e.g. at start/end/center).
---
### Author:  [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)
#### Post date: [January 23, 2024, 2:47pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/8 "2024-01-23T14:47:07Z")
With the default lags used in corrcor, the zero delay is in the center, so you could just subtract that index:
```julia
using StatsBase
T=0:0.1:10
X=sin.(T)
Y=sin.(T.-0.5)
z = StatsBase.crosscor(X, Y)
delay=argmax(z)
println(delay-div((size(z,1)+1),2))
```
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [January 23, 2024, 2:48pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/9 "2024-01-23T14:48:29Z")
Sorry, that doesn’t work.
---
### Author:  [@gabo-di](https://discourse.julialang.org/u/gabo-di)
#### Post date: [January 23, 2024, 2:56pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/10 "2024-01-23T14:56:36Z")
Something like this?
```julia
using StatsBase
function delay(x, y)
lags = (-length(y)+1):(length(x)-1)
z = crosscor(x, y, lags)
ind = argmax(z)
lags[ind]
end
```
but scipy’s correlate has more options, this is just an sketch.
---
### Author:  [@mgkuhn](https://discourse.julialang.org/u/mgkuhn)
#### Post date: [January 23, 2024, 3:05pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/11 "2024-01-23T15:05:08Z")
Ah, `StatsBase.crosscor` has a weird default range for `lags`, which you may need to override for longer inputs.
```julia
T=0:0.1:10
X=sin.(T)
Y=sin.(T.-0.5)
z = StatsBase.crosscor(X, Y, -(length(T)-1):(length(T)-1))
delay=argmax(z)-length(T)
5
```
But note that this may be biased in favour of large overlaps.
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [January 23, 2024, 3:29pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/12 "2024-01-23T15:29:55Z")
See also
> **[GitHub - baggepinnen/SignalAlignment.jl: Align signals to each other](https://github.com/baggepinnen/SignalAlignment.jl/)**
>
> Align signals to each other. Contribute to baggepinnen/SignalAlignment.jl development by creating an account on GitHub.
for more ways of computing the delay between signals
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [January 24, 2024, 7:39pm UTC](https://discourse.julialang.org/t/determine-the-delay-between-two-signals/109140/13 "2024-01-24T19:39:51Z")
The cross-correlation method presented above provides an integer delay (whole samples). To refine this and also obtain the fractional delay (fraction of a sample period), a simple method is to fit a parabola around the cross-correlation peak and obtain the abscissa of the apex.