# zerocrossrate

Zero-crossing rate

## Syntax

## Description

specifies additional name-value arguments. Use this syntax with any of the input arguments
in previous syntaxes.`rate`

= zerocrossrate(___,`Name,Value`

)

`zerocrossrate(___)`

with no output arguments plots
`rate`

along the *y*-axis and the corresponding
window number along the *x*-axis. If the window length is equal to the
full signal length, then the function plots the length of the window along the
*x*-axis and the crossing rate in the middle of the window.

## Examples

### Count Zero Crossings in Signal

Consider a vector of ones with alternating signs. Plot the data.

x = [1 -1 1 -1 1 -1 1 -1 1 -1]; plot(x)

Compute the zero-crossing rate of `x`

.

r = zerocrossrate(x)

r = 0.9500

Use the third output argument to find the locations where the crossings occur. Plot `x`

and the zero-crossing locations. The function returns an index at the next sample after a crossing, not necessarily the exact crossing location. The first sample is marked as a crossing point because the function considers the initial state of `x`

to be zero by default.

[~,~,indices] = zerocrossrate(x); plot(x) hold on plot(x(indices),'*') hold off

Compute the zero-crossing rate of `x`

using the comparison method. The rate differs from the value computed using the difference method.

`rC = zerocrossrate(x,Method="comparison")`

rC = 0.9000

Compute the zero-crossing rate of `x`

again using the difference method and specify zero as positive. The rate is equal to the value computed using the comparison method.

rZ = zerocrossrate(x,ZeroPositive=1)

rZ = 0.9000

Now specify the initial state of `x`

as `1`

. The rate is equal to the previous result.

rI = zerocrossrate(x,InitialState=1)

rI = 0.9000

### Count Level Crossings in Temperature Data

Load a set of temperature readings in Celsius taken every hour at Logan Airport in Boston for the entire month of January, 2011. Create a `timetable`

and use `retime`

to aggregate the data into daily means.

load bostemp t = hours(1:24*31)'; TT = timetable(t,tempC); rTT = retime(TT,'daily','mean');

Count the number of days the temperature crosses the monthly average. Plot the data and include a horizontal line at the monthly average temperature to visualize where the crossings occur.

avg = mean(TT.tempC)

avg = -1.3007

[~,count] = zerocrossrate(rTT,Level=avg)

count = 9

plot(hours(rTT.t/24),rTT.tempC) yline(avg) xlabel('Time elapsed since January 1, 2011 (days)') ylabel('Average daily temperature (\circC)') axis tight

### Identify Voiced and Unvoiced Speech Using Zero Crossings

Speech can be characterized as being voiced or unvoiced. *Voiced* speech, such as vowel sounds, occurs when the vocal cords vibrate. In *unvoiced* speech, such as most consonant sounds, the vocal chords do not vibrate. You can use zero crossings to classify the voiced and unvoiced regions in an audio signal.

Load an audio signal into the MATLAB® workspace. The voice says, "Oak is strong, and also gives shade".

[y,fs] = audioread("oak.m4a"); % To hear, type soundsc(y,fs)

The signal is sampled at 44.1 kHz. Calculate the zero-crossing rate for 10 ms windows using the comparison method.

```
win = fs*0.01;
rate = zerocrossrate(y,WindowLength=win,Method="comparison");
```

Plot `rate`

to visualize the crossing rate for each segment. Voiced speech is expected to have a low crossing rate, while unvoiced speech is expected to have a high crossing rate.

plot(rate)

Use a threshold of `0.1`

to differentiate between voiced and unvoiced segments. Create a `signalMask`

object that has two categories ("Unvoiced" and "Voiced") and plot the regions of interest (ROIs). Compare the regions of voiced and unvoiced speech to the location of each spoken word.

You can use Audio Toolbox™ speech-to-text functionality to extract words from an audio file. Load the labeled signal set `ls`

from `SpeechTranscription.mat`

into the workspace. The labeled signal set contains the audio signal, ROI limits, and labels for each spoken word. For more information on labeling audio signals, see Label Spoken Words in Audio Signals. Display the spoken words on the plot.

h = 0.1; idu = find(rate > h); idu(1:2) = []; vi = [(idu-1) idu]*win; m = sigroi2binmask(vi,length(y)); mask = signalMask([m ~m],Categories=["Unvoiced" "Voiced"],SampleRate=fs); plotsigroi(mask,y) load SpeechTranscription ln = getLabelNames(ls); v = getLabelValues(ls,1,ln); v.Value = categorical(v.Value,v.Value); RL = v.ROILimits; VL = v.Value; hold on text(mean(RL,2),-0.7*ones(size(VL)),VL,HorizontalAlignment="center", ... FontSize=11,FontWeight="bold") hold off

### Zero-Crossing Rate of Streaming Data

Load an audio file containing 15 seconds of acoustic guitar music. The sample rate is 44.1 kHz. To play the music, uncomment the last line of code.

Fs = 44100; y = audioread("guitartune.wav"); % sound(y,Fs)

Buffer the audio signal into overlapping frames, each with 4096 samples. Use an overlap of 512 samples.

```
winLength = 4096;
overlap = 512;
[yB,~] = buffer(y,winLength,overlap,"nodelay");
```

Obtain the zero-crossing rate for each frame. To account for frame overlap, specify the initial state as the previous value of the first sample in each frame.

init = winLength - overlap; state = 0; zcr = []; for i = 1:size(yB,2) zcr = [zcr;zerocrossrate(yB(:,i),InitialState=state)]; state = yB(init,i); end

Plot the audio signal and overlay the zero-crossing rate for each frame.

figure yyaxis left x = 0:1/Fs:(numel(y)-1)/Fs; plot(x',y) xlabel("Seconds") ylabel("Amplitude") yyaxis right xx = (1:size(yB,2))*((winLength-overlap)/Fs); plot(xx',zcr) ylabel("Zero-crossing rate")

Compute the zero-crossing rate of the unbuffered signal. To obtain a result equivalent to the zero-crossing rate of the buffered signal, set `WindowLength`

to `4096`

and `OverlapLength`

to `512`

. Determine if the two results are equal.

zcr_batch = zerocrossrate(y,WindowLength=winLength,OverlapLength=overlap); isequal(zcr_batch,zcr)

`ans = `*logical*
1

## Input Arguments

`x`

— Data

real-valued vector | real-valued matrix

Data, specified as a real-valued vector or matrix. If `x`

is a
matrix, the function returns the zero-crossing rate as a row vector where each value
corresponds to a column of data.

**Data Types: **`single`

| `double`

`TT`

— Input timetable

timetable

Input timetable, specified as a `timetable`

.
`TT`

must contain uniformly sampled single- or double-precision
data. The RowTimes property must
contain a `duration`

or `datetime`

vector with increasing and finite values. If `TT`

is a timetable with
a single variable containing a matrix, or a timetable with multiple variables each
containing a vector, then the function analyzes each channel independently.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`zerocrossrate(x,Method="comparison",Level=7,transitionEdge="rising")`

uses the comparison method to compute the rate at which `x`

positively
transitions across `7`

.

`InitialState`

— Previous states

`0`

(default) | vector

Previous states of `x`

, specified as a vector whose number of
elements is equal to the number of input channels.

**Example: **`zerocrossrate(x,InitialState=[1 0 –1 3])`

returns the
crossing rates of a four-channel input signal `x`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`Method`

— Method for computing zero-crossing rate

`"difference"`

(default) | `"comparison"`

Method for computing the zero-crossing rate, specified as
`"difference"`

or `"comparison"`

. If you do not
specify `Method`

, the function uses the difference method to
compute the crossing rate.

`comparison`

— The function marks the`indices`

as true where a crossing is fully completed.`difference`

— The function marks the`indices`

as true where abs(sign(*x*_{i})–sign(*x*_{i–1})) > 0.

**Example: **`zerocrossrate(x,Method="comparison")`

computes the
crossing rate of `x`

using the comparison method.

**Data Types: **`char`

| `string`

`WindowLength`

— Window length

positive integer

Window length over which to compute the crossing rate, specified as a positive integer. The default window length is the signal length.

**Example: **`zerocrossrate(x,WindowLength=20)`

returns the crossing
rates for 20-sample windows in `x`

.

**Example: **`zerocrossrate(x,WindowLength=fs*0.05)`

returns the
crossing rates for 50 ms windows in `x`

given a sample rate
`fs`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`OverlapLength`

— Number of overlapping samples

`0`

(default) | positive integer

Number of overlapping samples between adjoining segments, specified as a positive integer. The overlap must be smaller than the window length.

**Example: **`zerocrossrate(x,OverlapLength=0)`

returns the crossing
rates of segments with no overlap.

**Example: **`zerocrossrate(x,WindowLength=20,OverlapLength=5)`

returns the crossing rates of overlapping segments with five samples of
overlap.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`Level`

— Signal level

`0`

(default) | real scalar

Signal level for which the crossing rate is computed, specified as a real scalar.
The function subtracts the `Level`

value from the signal and then
finds the zero crossings. If you do not specify `Level`

, the
function uses the default value of `0`

and returns the zero-crossing
rate.

**Example: **`zerocrossrate(x,Level=1)`

returns the rate at which the
input signal `x`

crosses `1`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`Threshold`

— Threshold

`0`

(default) | real scalar

Threshold value above and below the `Level`

value over which
the crossing rate is computed, specified as a real scalar. The function sets all the
values of the input in the range [–`threshold`

,
`threshold`

] to `0`

and then finds the zero
crossings.

**Example: **`zerocrossrate(x,Threshold=0.1)`

returns the crossing
rate with a tolerance of –0.1 to 0.1.

**Note**

When you specify both `Level`

and
`Threshold`

, the function first subtracts the level value from
the input and then sets to `0`

the resulting input values that are
in the range [–`threshold`

, `threshold`

].

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`TransitionEdge`

— Transitions

`"both"`

(default) | `"falling"`

| `"rising"`

Transitions to include when counting the zero crossings, specified as
`"falling"`

, `"rising"`

, or
`"both"`

. If you specify `"falling"`

, the function
counts only negative-going transitions. If you specify `"rising"`

,
the function counts only positive-going transitions.

**Example: **`zerocrossrate(x,TransitionEdge="rising")`

returns the
crossing rate of `x`

for only positive-going
transitions.

**Data Types: **`char`

| `string`

`ZeroPositive`

— Sign convention

`0`

or `false`

(default) | `1`

or `true`

Sign convention, specified as a logical scalar. If you specify
`ZeroPositive`

as true, the function considers
`0`

to be positive. If you specify
`ZeroPositive`

as false, the function considers
`0`

, –`1`

, and +`1`

to have
distinct signs following the convention of the `sign`

function.

**Example: **`zerocrossrate(x,ZeroPositive=1)`

returns the crossing
rate of the input signal `x`

and considers zero as
positive.

**Data Types: **`logical`

## Output Arguments

`rate`

— Zero-crossing rate

row vector | matrix

Zero-crossing rate, returned as a row vector or a matrix. When
`WindowLength`

is equal to the signal length,
`rate`

is a row vector whose number of elements is equal to the
number of channels in `x`

or `TT`

. When
`WindowLength`

is smaller than the signal length, the function
returns `rate`

as a matrix where the *i*-th row
contains the crossing rate for the *i*-th window and the
*j*-th column corresponds to the *j*-th input
channel.

`count`

— Number of crossings

*N*-by-*M* matrix

Number of crossings, returned as an *N*-by-*M*
matrix where *N* is the number of windows and *M* is
the number of input channels. The *i*-th row corresponds to the
crossing count for the *i*-th window and the
*j*-th column corresponds to the crossing count for the
*j*-th channel.

`indices`

— Logical indices

*N*-by-`WindowLength`

-by-*M*
array

Logical indices at the signal locations where crossings occur, returned as an
*N*-by-`WindowLength`

-by-*M*
array where *N* is the number of windows and *M* is
the number of input channels.

**Note**

Indices might not represent exact signal crossing locations. The
`zerocrossrate`

function returns an index at the next sample
following a crossing.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation does not support disabling dynamic memory allocation when the window length is specified and the input is more than one channel.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## Version History

**Introduced in R2021b**

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