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SignalProcessing

  

RealCepstrum

  

compute the real cepstrum of the signal

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

RealCepstrum(A)

Parameters

A

-

Array of real numeric values; the signal

Description

• 

The RealCepstrum(A) command computes the real logarithm of the magnitude of the Fourier transform of a sequence.

• 

A must be a one-dimensional Array and must contain real numbers only.

Examples

withSignalProcessing:

We will artificially pollute a signal with an echo. The Cepstrum command will then be used to identify the location of the echo.

Fs100:

tStart0:

tEnd15:

tEcho4.5:

NtEndtStartFs+1:

Define a clean, unpolluted signal:

tVectorseqi,i=tStart..tEnd,1.0Fs:

cleanSignal`~`:-`/``~`sin2Pi1.3t,` $`,`~`:-`+`t,` $`,10+`~`:-`/``~`cos2Pi2.4t,` $`,`~`:-`+`t,` $`,10:

cleanSignalPlotplott,cleanSignal,legend=Clean Signal

The echo is the original signal, delayed by tEcho.

echoSignalVector0$floorFstEcho+1,cleanSignal1..NfloorFstEcho+1:

The dirty signal is the clean signal plus the echo multiplied by a small factor:

dirtySignalcleanSignal+0.3echoSignal:

dirtySignalPlotplott,dirtySignal,color=blue,legend=Signal with Echo

rRealCepstrumdirtySignal:

plott,r,view=tStart..tEnd,1.5..1

The peak in the cepstrum plot shows the location of the echo. Find the sample at which the echo occurs.

thresholdmapx&rarr;piecewisex<0.2&comma;0&comma;1&comma;r&colon;

indArrayTools:-SearchArraythreshold&comma;5&colon;

The echo starts at sample 452 and a time of t[452]

t452

4.510000000

(1)

Now use this information to generate an IIR filter to remove the echo.

filteredSignalSignalProcessing:-FilterdirtySignal&comma;Array1&comma;0&dollar;450&comma;0.35&comma;Array1&colon;

filteredSignalPlotplott&comma;filteredSignal&comma;color&equals;black&comma;legend&equals;Filtered Signal

plots:-displaydirtySignalPlot&comma;filteredSignalPlot

plots:-displaycleanSignalPlot&comma;filteredSignalPlot

Compatibility

• 

The SignalProcessing[RealCepstrum] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

SignalProcessing

SignalProcessing[ComplexCepstrum]