# rpmfreqmap

Frequency-RPM map for order analysis

## Syntax

## Description

returns
the frequency-RPM map matrix, `map`

= rpmfreqmap(`x`

,`fs`

,`rpm`

)`map`

, that results
from performing frequency analysis on the input vector, `x`

. `x`

is
measured at a set `rpm`

of rotational speeds expressed
in revolutions per minute. `fs`

is the sample rate
in Hz. Each column of `map`

contains root-mean-square
(RMS) amplitude estimates of the spectral content present at each
value of `rpm`

. `rpmfreqmap`

uses
the short-time Fourier transform to analyze the spectral content of `x`

.

specifies
options using `map`

= rpmfreqmap(___,`Name,Value`

)`Name,Value`

pairs in addition to
the input arguments in previous syntaxes.

`rpmfreqmap(___)`

with no output
arguments plots the frequency map as a function of rotational speed
and time on an interactive figure. The plot is also known as a *Campbell
diagram*.

## Examples

### Frequency-RPM Map of Chirp with 4 Orders

Create a simulated signal sampled at 600 Hz for 5 seconds. The system that is being tested increases its rotational speed from 10 to 40 revolutions per second during the observation period.

Generate the tachometer readings.

fs = 600; t1 = 5; t = 0:1/fs:t1; f0 = 10; f1 = 40; rpm = 60*linspace(f0,f1,length(t));

The signal consists of four harmonically related chirps with orders 1, 0.5, 4, and 6. The order-4 chirp has twice the amplitude of the others. To generate the chirps, use the trapezoidal rule to express the phase as the integral of the rotational speed.

o1 = 1; o2 = 0.5; o3 = 4; o4 = 6; ph = 2*pi*cumtrapz(rpm/60)/fs; x = [1 1 2 1]*cos([o1 o2 o3 o4]'*ph);

Visualize the frequency-RPM map of the signal.

rpmfreqmap(x,fs,rpm)

### Frequency-RPM Map of Helicopter Vibration Data

Analyze simulated data from an accelerometer placed in the cockpit of a helicopter.

Load the helicopter data. The vibrational measurements, `vib`

, are sampled at a rate of 500 Hz for 10 seconds. Inspection of the data reveals that it has a linear trend. Remove the trend to prevent it from degrading the quality of the frequency estimation.

```
load('helidata.mat')
vib = detrend(vib);
```

Plot the nonlinear RPM profile. The rotor runs up until it reaches a maximum rotational speed of about 27,600 revolutions per minute and then coasts down.

plot(t,rpm) xlabel('Time (s)') ylabel('RPM')

Compute the frequency-RPM map. Specify a resolution bandwidth of 2.5 Hz.

[map,freq,rpmOut,time] = rpmfreqmap(vib,fs,rpm,2.5);

Visualize the map.

imagesc(time,freq,map) ax = gca; ax.YDir = 'normal'; xlabel('Time (s)') ylabel('Frequency (Hz)')

Repeat the computation using a finer resolution bandwidth. Plot the map using the built-in functionality of `rpmfreqmap`

. The gain in frequency resolution comes at the expense of time resolution.

rpmfreqmap(vib,fs,rpm,1.5);

### Waterfall Plot of Frequency-RPM Map

Generate a signal that consists of two linear chirps and a quadratic chirp, all sampled at 600 Hz for 15 seconds. The system that produces the signal increases its rotational speed from 10 to 40 revolutions per second during the testing period.

Generate the tachometer readings.

fs = 600; t1 = 15; t = 0:1/fs:t1; f0 = 10; f1 = 40; rpm = 60*linspace(f0,f1,length(t));

The linear chirps have orders 1 and 2.5. The component with order 1 has half the amplitude of the other. The quadratic chirp starts at order 6 and returns to this order at the end of the measurement. Its amplitude is 0.8. Create the signal using this information.

o1 = 1; o2 = 2.5; o6 = 6; x = 0.5*chirp(t,o1*f0,t1,o1*f1)+chirp(t,o2*f0,t1,o2*f1) + ... 0.8*chirp(t,o6*f0,t1,o6*f1,'quadratic');

Compute the frequency-RPM map of the signal. Use the peak amplitude at each measurement cell. Specify a resolution of 6 Hz. Window the data with a flat top window.

[map,fr,rp] = rpmfreqmap(x,fs,rpm,6, ... 'Amplitude','peak','Window','flattopwin');

Draw the frequency-RPM map as a waterfall plot.

[FR,RP] = meshgrid(fr,rp); waterfall(FR,RP,map') view(-6,60) xlabel('Frequency (Hz)') ylabel('RPM') zlabel('Amplitude')

### Interactive Frequency-RPM Map

Plot an interactive frequency-RPM map by calling `rpmfreqmap`

without
output arguments.

Load a file containing simulated vibrational data from an accelerometer placed in the cockpit
of a helicopter. The data is sampled at a rate of 500 Hz for 10 seconds.
Remove the linear trend in the data. Call `rpmfreqmap`

to
generate an interactive plot of the frequency-RPM map. Specify a frequency
resolution of 2
Hz.

```
load helidata.mat
rpmfreqmap(detrend(vib),fs,rpm,2)
```

Move the crosshair cursors in the figure to determine the RPM and the RMS amplitude at a frequency of 25 Hz after 5 seconds.

Click the **Zoom X** button in the toolbar to zoom into the time
region between 2 and 4 seconds. A panner appears in the bottom
plot.

Click the **Waterfall Plot** button
in the toolbar to display the
frequency-RPM map as a waterfall plot. For improved visibility, rotate the
plot clockwise using the **Rotate Left** button
three times. Move the panner to the
interval between 4 and 6 seconds.

## Input Arguments

`x`

— Input signal

vector

Input signal, specified as a row or column vector.

**Example: **`cos(pi/4*(0:159))+randn(1,160)`

specifies
a sinusoid embedded in white Gaussian noise.

`fs`

— Sample rate

positive scalar

Sample rate, specified as a positive scalar expressed in Hz.

`rpm`

— Rotational speeds

vector of positive values

Rotational speeds, specified as a vector of positive values expressed in revolutions per
minute. `rpm`

must have the same length as `x`

.

**Example: **`100:10:3000`

specifies that a system
rotates initially at 100 revolutions per minute and runs up to 3000
revolutions per minute in increments of 10.

`res`

— Resolution bandwidth

`fs`

/128 (default) | positive scalar

Resolution bandwidth of the frequency-RPM map, specified as
a positive scalar. If `res`

is not specified, then `rpmfreqmap`

sets
it to the sample rate divided by 128. If the signal
is not long enough, then the function uses the entire signal length
to compute a single frequency estimate.

**Data Types: **`single`

| `double`

### 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: **`'Scale','dB','Window','hann'`

specifies
that the frequency map estimates are to be scaled in decibels and
determined using a Hann window.

`Amplitude`

— Frequency-RPM map amplitudes

`'rms'`

(default) | `'peak'`

| `'power'`

Frequency-RPM map amplitudes, specified as the comma-separated
pair consisting of `'Amplitude'`

and one of `'rms'`

, `'peak'`

,
or `'power'`

.

`'rms'`

— Returns the root-mean-square amplitude for each estimated frequency.`'peak'`

— Returns the peak amplitude for each estimated frequency.`'power'`

— Returns the power level for each estimated frequency.

`OverlapPercent`

— Overlap percentage between adjoining segments

50 (default) | scalar from 0 to 100

Overlap percentage between adjoining segments, specified as
the comma-separated pair consisting of `'OverlapPercent'`

and
a scalar from 0 to 100. A value of 0 means that adjoining segments
do not overlap. A value of 100 means that adjoining segments are shifted
by one sample. A larger overlap percentage produces a smoother map
but increases the computation time. See `rpmordermap`

for
more information.

**Data Types: **`double`

| `single`

`Scale`

— Frequency-RPM map scaling

`'linear'`

(default) | `'dB'`

Frequency-RPM map scaling, specified as the comma-separated
pair consisting of `'Scale'`

and either `'linear'`

or `'dB'`

.

`'linear'`

— Returns a linearly scaled map.`'dB'`

— Returns a logarithmic map with values expressed in decibels.

`Window`

— Analysis window

`'hann'`

(default) | `'chebwin'`

| `'flattopwin'`

| `'hamming'`

| `'kaiser'`

| `'rectwin'`

Analysis window, specified as the comma-separated pair consisting
of `'Window'`

and one of these values:

`'hann'`

specifies a Hann window. See`hann`

for more details.`'chebwin'`

specifies a Chebyshev window. Use a cell array to specify a sidelobe attenuation in decibels. The sidelobe attenuation must be greater than 45 dB. If not specified, it defaults to 100 dB. See`chebwin`

for more details.`'flattopwin'`

specifies a flat top window. See`flattopwin`

for more details.`'hamming'`

specifies a Hamming window. See`hamming`

for more details.`'kaiser'`

specifies a Kaiser window. Use a cell array to specify a shape parameter,*β*. The shape parameter must be a positive scalar. If not specified, it defaults to 0.5. See`kaiser`

for more details.`'rectwin'`

specifies a rectangular window. See`rectwin`

for more details.

**Example: **`'Window','chebwin'`

specifies a Chebyshev
window with a sidelobe attenuation of 100 dB.

**Example: **`'Window',{'chebwin',60}`

specifies
a Chebyshev window with a sidelobe attenuation of 60 dB.

**Example: **`'Window','kaiser'`

specifies a Kaiser
window with a shape parameter of 0.5.

**Example: **`'Window',{'kaiser',1}`

specifies
a Kaiser window with a shape parameter of 1.

**Data Types: **`char`

| `string`

| `cell`

## Output Arguments

`map`

— Frequency-RPM map

matrix

Frequency-RPM map, returned as a matrix.

`freq`

— Frequencies

vector

Frequencies, returned as a vector.

`rpm`

— Rotational speeds

vector

Rotational speeds, returned as a vector.

`time`

— Time instants

vector

Time instants, returned as a vector.

`res`

— Resolution bandwidth

scalar

Resolution bandwidth, returned as a scalar.

## References

[1] Brandt, Anders. *Noise and Vibration Analysis:
Signal Analysis and Experimental Procedures*. Chichester,
UK: John Wiley & Sons, 2011.

## Extended Capabilities

### C/C++ Code Generation

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

## Version History

**Introduced in R2015b**

## See Also

`orderspectrum`

| `ordertrack`

| `orderwaveform`

| `rpmordermap`

| `rpmtrack`

| `spectrogram`

| `tachorpm`

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