Application
note # 15 
Sample
Champion

Enhanced View Plugin:
ETC, Spectrogram, Nyquist Plot...
This application note describes the use of the Sample Champion
Enhanced View Plugin. This module gets the current Impulse
Response (1 or 2 channels).
Enhanced
View Plugin. Spectrogram of Example1.ire file
An
Impulse Response must be loaded or measured and one of two data
selections (A and/or B) must be enabled in
Sample Champion. Now the
Enhanced View Plugin can be opened.
The
frequency analysis performed by this module is driven by the
data windowing (Selections A and B) and FFT settings (FFT size
and window type) of the main program. Selections A and B can
be assigned to channel 1 or 2 of the Impulse
Response (if stereo) from the plugin. Moreover the frequency
data of the 2 selections can be plotted simultaneously selecting
"FFT of Selection A and B".
The button marked "W" inside the "Frequency Range"
box sets automatically the lower frequency of the plot according
with the resolution due to the data windowing length.
Remember that the lower resolution limit depends (for every
measurement method) on the weighting window length and type.
The rectangular window has a frequency resolution of 1/T Hz,
the BlackmanHarris about twice.
The
computed phase can be plotted in 3 different ways:
 Measured phase (wrapped or unwrapped)
 Minimum phase (always unwrapped)
 Excess phase
(always unwrapped)
Note
that the minimum and excess phase algorithm requires intensive
computations, so data selections in the main program must be
moved or changed with care when one of these view modes is selected.
Minimum
Phase Impulse Response of data inside Selection A can be
computed and plotted by pressing the button "View Minimum
Phase I.R.". This works only for mono impulse responses
or for channel 1 of stereo impulse responses. The minimum phase
recostruction (used also for minimum and excess phase computation
of Selections A and B) is obtained by means of cepstral analysis.
If
h is a vector containing the windowed impulse response
then:
Cepstrum = IFT(log(abs(FFT(h))))
Only
the causal part is retained from the Cepstrum vector,
by zeroing its second half (obtaining Cepstrum2). The
minimum phase Impulse Response is obtained by means of the following
operation:
MinPh
= IFT(exp(FFT(Cepstrum2)))
To
obtain the minimum phase spectral data, the MinPh
impulse response is computed and analyzed with current FFT settings.
Data windowing in this case starts from t=0 (because homomorphic
reconstruction moves the beginning of the obtained impulse to
t=0) and has the same length of the current Data Selection (A
or B).
Excess
phase is simply the difference between (unwrapped) measured
phase and minimum phase.
Example
of minimum phase spectral data of Selections A and B (green=channel
1, red=channel 2)
Example
of excess phase spectral data of Selections A and B
Frequency
data can be viewed also in the form of Nyquist plot.
This view mode plots Real and Imaginary data respectively on
X and Y axes. By mousedragging the bar under the graphic plot,
the data values can be visualized.
Example
of Nyquist plot (Selections A and B)
The
2 following figures show an example of Nyquist Plot of a loopback
impulse response before and after Pink Filtering.
Example
of Nyquist plot of a loopback measurement
before and after Pink Filtering
The
Spectrogram function computes and plots the distribution
of the frequency content of the Impulse Response along the time
axis. Time is reported on the X axis, frequency on Y axis, color
denotes dB power spectrum levels (red=higher, blu=lower). Every
slice (vertical line) is obtained by computing the FFT of the
data windowed around the considered time position. The spectrogram
FFT length and window type are independent from the main program
settings and can be set by the user. The "Overlap"
percentage indicates the overlapping factor between adjacent
data windowings.
A
proper setting of spectrogram options requires some training
and testing. Every Impulse Response has different characteristics
and requires specific values of FFT length, Window and Overlap
percentage.
Some
tests can be performed by pressing the "Plot First and
Peak Slices" button: the slice centered at t=0 and the
slice centered at the time location of the Impulse Response
peak will be plotted. Then the Top and Range of the graph and
the frequency lower and upper limits can be set. It is suggested
to set linear frequency view mode.
As first choice, the "Plot WHOLE Spectrogram" button
can be pressed (with "Plot ALL" option unchecked).
This will plot only the first slices (the number can be set).
When you are satisfied with the result, the "Plot ALL"
option can be checked and finally, pressing the "Plot WHOLE
Spectrogram" button, the whole spectrogram will be plotted.
CAUTION: depending on the settings, the spectrogram could
require much time to be plotted, because several hundred or
thousands of FFTs must be computed. So the "Plot ALL"
option must be checked only when you are sure that every parameter
is right.
The
spectrogram shown above is obtained from Example1.ire file (a
Loudspeaker Impulse Response) with the following settings:
 Top Graph=23 dB
 Range Graph=105 dB
 Spectrogram FFT size=512 points
 Overlap=99%
A first reflection is clearly visible in the proximity of t=50
ms.
The
2 figures below plot a 256K room Impulse Response measured in
a large hall. The settings for computing this spectrogram are
the following:

Top Graph=16 dB
 Range Graph=115 dB
 Spectrogram FFT size=2048 points
 Overlap=87%
Spectrogram
of a large hall impulse response
Zoom
of the above Spectrogram (first 1000 ms)
Also
the Energy Time Curve of time data can be plotted. ETC
is similar to the Log Squared view mode available in the Room
Acoustics plugin, but is computed by means of the Hilbert Transform
of the Impulse Response.
Example
of ETC curve (2 channels)
Download
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