Engee documentation

alignsignals

Aligns the two signals by delaying the earliest signal.

Library

EngeeDSP

Syntax

Function call

  • xa, ya, D = alignsignals(x, y) — evaluates the delay D between two input signals x and y and returns D together with the aligned signals xa and ya. The function estimates the delay using cross-correlation.

    • If y detained relatively x Then D Positively, eh x detained on D counts.

    • If y ahead of x Then D negative, eh y detained on −D counts.

    The input signals do not have to be exact retarded copies of each other. However, the signals can only be precisely aligned if there is sufficient correlation between them. For more information about estimating covariance and correlation, see [1].

  • xa, ya, D = alignsignals(x, y, Name=Value) — also uses arguments Name=Value, which include an estimation method and an option for truncating input signals. For example, to estimate the delay based on the location of the largest peak in each signal, set for the argument Method meaning "maxpeak".

Arguments

Input arguments

# x is the first input signal

+ vector

Details

The first input signal, specified as a numeric vector of length .

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Support for complex numbers

Yes

# y is the second input signal

+ vector

Details

The second input signal, specified as a numeric vector of length .

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Support for complex numbers

Yes

Name-value input arguments

Specify optional argument pairs in the format Name=Value, where Name — the name of the argument, and Value — the appropriate value. Type arguments Name=Value they should be placed after the other arguments, but the order of the pairs does not matter.

# Method is a method for estimating the delay between signals

+ "xcorr" (by default) | "maxpeak" | "npeak" | "risetime"

Details

A method for estimating the delay between signals specified as "xcorr", "maxpeak", "npeak" or "risetime". You can specify additional name-value arguments depending on the specified Method:

  • "xcorr" — delay estimation using cross-correlation. If the method is specified as "xcorr", then you can also specify MaxLag;

  • "maxpeak" — Delay estimation using the position of the highest peak in each signal. If the method is specified as "maxpeak", then you can additionally specify MinPeakProminence and MinPeakHeight;

  • "npeak" — estimation of delay using position -th peak in each signal. If the method is specified as "npeak", then you can additionally specify PeakNum, MinPeakProminence and MinPeakHeight;

  • "risetime" — delay estimation using the position of the rising edges in each signal. The function uses the specified values StateLevels to search for rising fronts.

# MaxLag — maximum window size

+ scalar

Details

The maximum window size used to estimate the delay between signals is set as an integer scalar. By default MaxLag equal to , where — length x, and — length y. If MaxLag if it is negative, then the function uses the absolute value.

This argument is used only if for the argument Method the value is set "xcorr".

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

# PeakNum — peak number

+ scalar

Details

The peak number used to equalize the signals is set as a positive integer scalar. This argument is used only if for the argument Method the value is set "npeak".

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

# MinPeakProminence — minimum peak elevation

+ scalar

Details

The minimum peak elevation used to identify peaks in the signals is given as a real non-negative scalar. When specifying MinPeakProminence The function finds peaks whose relative importance is not less than the specified value. For more information, see the section Elevations.

This argument is used only if for the argument Method the value is set "npeak" or "maxpeak".

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

# MinPeakHeight — minimum peak height

+ scalar

Details

The minimum peak height used to determine the peaks in the signals is given as a real scalar. When specifying MinPeakHeight the function finds peaks whose height exceeds the specified value. For more information, see findpeaks.

This argument is used only if for the argument Method the value is set "npeak" or "maxpeak".

Типы данных

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

# StateLevels — state levels

+ A two-element vector is a string

Details

The state levels are specified as a real two-element vector string. The first element corresponds to the low state level of the input signals, and the second element corresponds to the high state level of the input signals. If the value is StateLevels If not specified, the function evaluates the state levels of the input signal using the histogram method.

For more information, see risetime.

This argument is used only if for the argument Method the value is set "risetime".

Типы данных

Float64

# Truncate — option for truncating input signals

+ false (0) (by default) | true (1)

Details

The option of truncating input signals, set by numeric or logical true (1) or false (0). When specifying the value true (1) for the argument Truncate lengths xa and ya equal to the lengths x and y accordingly.

  • If the estimated delay is D if it is positive, then the function adds D zeros to x and truncates the last ones D counts x.

  • If D if it is negative, then the function adds −D zeros to y and truncates the last ones D counts y.

  • If D Then xa consists of zeros, and all counts x they get lost. If −D Then ya consists of zeros, and all counts y they get lost.

Output arguments

# xa — aligned first signal

+ vector

Details

The aligned first signal returned as a numeric vector aligned with the second output argument ya.

  • If the input argument is x — a vector is a string, then xa It is also a string vector.

  • If the input argument is x is a column vector, then xa It is also a column vector.

If for an argument Truncate the value is set true, and the estimated delay D If it is positive, then xa is equivalent to the input signal x with D with added zeros and truncated last ones D by counting down.

# ya — aligned second signal

+ vector

Details

The aligned second signal returned as a numeric vector aligned with the second output argument xa.

  • If the input argument is y — a vector is a string, then ya It is also a string vector.

  • If the input argument is y is a column vector, then ya It is also a column vector.

If for an argument Truncate the value is set true, and the estimated delay D if it is negative, then ya is equivalent to the input signal y with −D with added zeros and truncated last ones −D by counting down.

# D is the calculated delay between the input signals

+ an integer scalar

Details

The calculated delay between the input signals, returned as an integer scalar. This value represents the number of samples by which the two input signals are offset. x and y.

  • If y lags behind relatively x Then D Positively, eh x lags by D counts.

  • If y ahead of x Then D negative, eh y lags by −D counts.

  • If x and y already aligned, then D is equal to zero, and neither x, neither y They don’t linger.

If the value of the input argument is specified MaxLag Then D will be less than or equal to MaxLag.

Examples

Equalization of two signals if the first signal is three samples behind

Details

Create two signals: x and y. The signal x — it’s the same as y, except that you have x There are three zeros at the beginning and one extra at the end. Align the two signals.

import EngeeDSP.Functions: alignsignals

x = [0, 0, 0, 1, 2, 3, 0, 0]
y = [1, 2, 3, 0]

xa, ya, D = alignsignals(x, y)
(xa = [0, 0, 0, 1, 2, 3, 0, 0], ya = [0, 0, 0, 1, 2, 3, 0], D = -3)

Equalization of two signals if the second signal is two samples behind

Details

Create two signals: x and y. The signal y — it’s the same as x, except that y it is delayed for two counts. Align the two signals.

import EngeeDSP.Functions: alignsignals

x = [1, 2, 3]
y = [0, 0, 1, 2, 3]

xa, ya, D = alignsignals(x, y)
(xa = [0, 0, 1, 2, 3], ya = [0, 0, 1, 2, 3], D = 2)

Align the signals using the maximum window size 1:

maxlag = 1
xa, ya, D = alignsignals(x, y, Method="xcorr", MaxLag=maxlag)
(xa = [0, 1, 2, 3], ya = [0, 0, 1, 2, 3], D = 1)

Alignment of two two-level signals along rising edges

Details

We will generate two signals representing two-level signals. The signals have a sampling frequency 50 Hz during 20 seconds. For the first signal, the transition occurs via 13 seconds after the start of the measurement. For the second signal, the transition occurs via 5 seconds after the start of the measurement. The signals have different amplitudes and are in white Gaussian noise with different variances. Let’s plot the signal graphs.

t = range(0, 20, length=1001)

e1 = 1.4 .* tanh.(t .- 13) .+ randn(length(t)) ./ 3
e2 = tanh.(3 .* (t .- 5)) .+ randn(length(t)) ./ 5

plot(t, e1, label="e1")
plot!(t, e2, label="e2")
xlabel!("Seconds")
ylabel!("Amplitude")

alignsignals 1

Align the signals so that their transition times match.

Correlation methods do not allow us to adequately align this type of signals.:

y1, y2 = alignsignals(e1, e2)

plot(y1, label="y1 (aligned e1)")
plot!(y2, label="y2 (aligned e2)")
xlabel!("Samples")
ylabel!("Amplitude")

alignsignals 2

Align the signals using the method "risetime":

y1, y2 = alignsignals(e1, e2, Method="risetime")

plot(y1, label="y1 (aligned e1)")
plot!(y2, label="y2 (aligned e2)")
xlabel!("Samples")
ylabel!("Amplitude")

alignsignals 3

Literature

  1. Orfanidis, Sophocles J. Optimum Signal Processing. An Introduction. 2nd Ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.