TFA -
Time frequency analysis
and
-modification
Software package: Version 2.033, 30.07.10
This documentation: 30.07.10
IND - Ingenieurbüro für Nachrichten- und Datentechnik
Dr.-Ing. Peer Dahl
Keplerstrasse 44
D-75175
Tel. 49-7231-650332
Fax: 49-7231-965186
eMail: P.Dahl@ind-technik.de
Internet: www.ind-technik.de
Preface
Honored customer,
honored user!
Many thanks, that you decided
for this software product worldwide unique according to current research for
the purpose of the time frequency analysis. As you certainly know, the special
thing of this program lies in the contained algorithms (calculation methods)
for the breakup of the general attachment between time and frequency
resolution, which seen physical is regarded as impossible up to now.
The today available
processing power allows both the development and then the use of algorithms,
which denote a significant progress here. These flowed into TFA
directly.
For interested: Some time-frequency
analysis theory – what’s it all about?
To gain deeper insight into
the frequency characteristic of signals the Discrete Fourier transform (DFT)
today surely is one of the most frequent and in all fields of Digital Signal Processing
used analytical tools. The spectral description of a process can in addition be
starting point for purposeful manipulations in the frequency domain as a useful
alternative to the processing in the time domain.
Phenomena to be examined in
practice are frequently of instationary nature and are available only for a
restricted time interval. Although the DFT is defined unlike the time-discrete
Fourier transform only for a temporary process, the measurement period,
necessary to obtain a certain frequency accuracy, can be still considerably too
large. Meanwhile in case of instationary processes the minimization of the measurement
period is to strive also for obtaining a satisfactory temporal localization of
the result. Under these conditions the DFT supplies only a more or less
indistinct estimate of the context.
Since Werner Heisenberg
formulated his famous uncertainty relation of the quantum mechanics in the year
1927, also its analogy in the communication engineering therefore remained of
special importance until today.
Its consequence for the
spectrum analysis is that the priority between achieved frequency accuracy on
the one hand and the temporal localization on the other hand is to be decided
on. Both information can not be given simultaneously “exactly”. If a spectrum
shall represent only a short time interval, a coarse frequency resolution is to
be reckoned. If one increases the requirement onto the frequency resolution,
this requires a correspondingly longer analysis time interval. The fundamental
relationship between these two terms can be numerated exactly and comprehended
with every spectrum analyzer - whichever the principle of operation is.
On on hand one became accustomed to this association today, on the other
hand the restrictions turning out are so serious that until today worldwide endeavour
is made to searched for new ways out. It is to be observed that solutions known
up to now
· show disturbing
side effects due to non-linearities as occurrence of cross products and phantom
signals that do not exist (e.g. in case of the Wigner-Ville approach),
· do not meet the claim
by a more precise consideration (e.g. in case of the Wavelet-transformation),
· to presuppose unrealistic
conditions (e.g. the use of Gabor coefficients) or
· require Apriori-knowledge
(e.g. Linear Predictive Coding, LPC)
and therefore their use is
possible only for selected fields of application.
TFA contains a new
solution, which does not have the known disadvantages or in decisively smaller
extent.
Now we wish you a lot of
success and new analysis epertise about your signals which never before were to
be achieved in this quality.
Yours
IND - Ingenieurbüro für Nachrichten- und Datentechnik
Dr.-Ing. Peer Dahl
Keplerstrasse 44
D-75175 Pforzheim
Tel. 49-7231-650332
Fax: 49-7231-965186
eMail: P.Dahl@ind-technik.de
Internet:
www.ind-technik.de
Inhalt
2 System requirements, installation
and deinstallation
2.2.2 For less practiced users
4.1 The work space with the
representations time domain, frequency domain and time-frequency domain
4.1.1 The representation „Time domain“
4.1.2 The representation „Frequency
domain“
4.1.3 The representation „Time-frequency
domain “
4.1.4 Selection and sizes of the
representations
4.2.1.1.1 WAV-Format, 16 Bit, 1 channel (mono)
4.2.1.1.2 WAV-Format, 16 Bit, 2 channell (complex)
4.2.1.1.3 WAV-Format, PCM, 24 Bit and 32 Bit, 1 channel and 2 channels
4.2.1.1.4 WAV-Format, FLOAT, 32 Bit, 1 Kanal
bzw. 2 Kanäle
4.2.1.1.5 TFA-Format, 32 Bit, 1 channel (real)
4.2.1.1.6 TFA-Format, 32 Bit, 2 channel (complex)
4.2.1.1.7 TXT-Format, Textfile
4.2.1.2 Export (complex) respectively Export (real)
4.2.3.1.1 Level-Colour-Assiociation
4.3.4 Presentation continuous /
discrete
4.3.10 Vertikal harmonic marker
4.3.11 Horizontal harmonic marker
4.3.12 Advanced XY-Marker functions
4.3.14 Advanced zoom/boundary functions
4.3.15 Spectrum analysis settings
4.3.15.6 Further explanation of the
settings
4.3.16.6 Lower level threshold
4.3.17 DDC – Digital Down Converter
4.3.17.4 Automatic setting of the DDC
5.1.1 Speech signal: F0-analysis in
natural language
5.1.2 Communication engineering:
FSK-signal with shift- and modulation rate measurement
5.2.1 Speech signal: Extraction of the
F0-oscillation
5.2.2 Communication engineering:
Extraction of a FSK-signal
5.3.1 Speech signal: Making audible a
discant voice component
5.3.2 Communication engineering:
Conversion of a real-valued signal into the complex base band
5.3.2.2 New TFA instance with DDC-result
5.4 Analysis of Modulation spectra
5.4.1 Selection and extraction of a
frequency component as its envelope
5.4.2 Analysis of the modulation spectrum
6 FAQ – Frequenzly asked questions
6.1 Uncoupling XY-Marker and mouse
pointer
6.2 Long duration of DXP-I-computation
6.4 Unsatisfactory spectral resolution
6.5 Staircase-shaped time signal after
DDC-decimation
6.6 Installation on a network drive
9.1 Layout of the TFA-File-Format
TFA
–
Time frequency analysis and
-modification
1
General
Primarily the software product TFA is used for time-frequency
analysis, that means the simultaneous description of a signal both in
direction of the time axis as also the frequency axis. That shows a
tridimensional representation, the spectrogram, at which the signal
energy is colored as a third dimension characterized (e.g. high energy: red,
low energy: blue to black). If the signal sample to be analyzed is something
audible, one mentions the spectrogram also „sonagram”.
Whether signals, however, come from the world of audible, whether they
represent physical or other scientific processes, or whether they are signals
from the sundry communication engineering, e.g. the digital radio, is
unimportant: In all cases conventional spectrographs can represent the time-frequency
domain only with the typical uncertainty according to Heisenberg’s
uncertainty relationship of communication engineering.
An example to that: In the following a speech sample[1] is analyzed with
a conventional Hann-windowed fast Fourier transform (FFT) with a length of
4096:
Figure 1‑1: Speech sample, transformation
FFT, FFT-length 4096
That offers a quite precise resolution into frequency direction (3,91
Hz), however, a
coarse temporal resolution (about 0,256 s). The speech pauses are very
blurredly represented.
The temporal resolution can be increased through decrease of the
FFT-length onto the value 512 by the factor 8 as following spectrogram shows.
That offers a correspondingly coarse resolution in frequency direction (31,25
Hz), for that, however, a more precise temporal resolution (about 0,032 s). Now
for example the speech pauses are more precisely represented.
Figure 1‑2: Speech sample, transformation FFT, FFT-length 512
With TFA the signal can be exactly surveyed both in frequency-
and also in time direction. That performs the new transformation method DXP-I
eligible instead of the FFT. With DXP the frequency resolution (up to 4096
lines) and the time interval coming in (e.g. 512 samples) can be adjusted
separately from each other as following spectrogram shows. In a way one obtains the best
from the two above representations:
Figure 1‑3: Speech sample, transformation DXP-I, FFT-length 4096, 512 samples
Also a considerably more precise energy measurement is accompanied by
the significantly sharper representation of the time-frequency domain because
the signal energy is not distributed so very much in the plain anymore.
Based on a more precise spectrogram also the signal modification is possible in the time-frequency domain with higher
quality. As described later, eligible areas can be extracted in the spectrogram
or can be time-/frequency-agile filtered.
Important notice:
TFA and DXP are new, still little spread tools, that are not - that
is preceded - difficult to master. However, a little bit of practice and also
knowledge and experience is useful in order to be able to draw the full benefit
from that. Who is not yet so familiar to DXP, the short chapter 5 “practices” is warmly recommended to. It offers an introduction
and is considered as a starting point for the exploration of the own signal
material.
2
System
requirements, installation and deinstallation
In this section you find out,
how the software TFA is put into- and removed from operation.
2.1
System requirements
The least system requirements
are:
- Operation system: Windows
XP (SP2) Windows Vista or Windows 7
- Internet-browser for the display of help-files
- Main memory: 512 MBS
- Hard disk place: 20 MByte
- Processor clock: 2 GHz
- 1 free USB port for the dongle (copying
protection stick)
TFA manages also with
smaller resources, nevertheless: The higher the processor clock is, the shorter
the program reaction times are, especially in the case of the
DXP-transformations. A bigger main memory facilitates the enlargement of the
program windows onto the faces of two monitors (dual monitoring mode) also in
case of high screen resolution from 1280 x 1024 pixels. A bigger main memory
also facilitates the operation with very large signal files.
Recommended is:
- Double core processor system (Dual-Core, Core
Duo) with 2x3 GHz clock frequency
- 1 or 2 GB main memory
- Graphic with high resolution (1280 x 1024)
Even if TFA can
currently only use one processor, in case of a multiprocessor system it is nevertheless
possible to start a second instance of TFA in parallel and independently
of each other. In addition the operating system reacts to other inputs more
quickly, because TFA does not “block” the system.
2.2
Installation
TFA is - how many
other
TFA is delivered as a
ZIP-archive. The ZIP-archive contains the folder „TFA", under that all
needed subdirectories and files lie.
For the installation the
ZIP-archive is to be unpacked into an arbitrary folder. To do this one extracts
the complete folder „TFA" including its subdirectories and files onto an
arbitrary place on the hard disk.
Notice: You must have
administrator-rights!
2.2.1
For expert users
Please copy the contents of
the ZIP archive under retention of the directory structure onto an arbitrary
place of your hard disk and plug in the USB dongle into a free USB port.
2.2.2
For less practiced users
Maybe you wish to save the
„TFA"-folders in a new subdirectory e.g. with the name „TimeFrequencyAnalysis".
Please proceed then in following steps:
Step 1: Creation of a
folder named „TimeFrequencyAnalysis " on the hard disk.
To
that
- one opens the Windows-Explorer e.g. with the key
combination „<Windows> + <E>",
- choose a folder on the wanted hard disk drive or
create one at a wanted folder place by pressing of the right mouse button,
then ->New->Folder. Now one enters e.g. „TimeFrequencyAnalysis
" and confirms that with the „return" –Key.
Step 2: Unpack the ZIP
archive into the before created folder. According to that, as you acquired the
TFA-ZIP archive,
- it is stored on a storage medium or
- lies as download e.g. in your download folder or
- is managed by your download-manager-software.
Please open the ZIP-archive
with a double-click with the left mouse button onto the ZIP-file or by clicking
onto the key „Proceed" (or comparably similar) in your download-manager.
The indicated contents of the
ZIP-archive are to be copied with the right mouse button and to be pasted into
the folder created in step 1.
Possibly you would like to
create further folders in the folder „TimeFrequencyAnalysis" e.g. for your
signal files. In this case your directory structure looks e.g. as follows:
Figure 2‑1: Possible directory structure for the program installation
Step 3: Plug in the
Dongle „TFA" into a free USB port.
Tip: The best choice is a
USB-port on the back of the computer so that a mechanical harm of the Dongle
and the computer while pushing inadvertent is avoided.
No automatic installations
occur while plugging in the Dongle
2.3
Installation of updates
Please simply copy new files
into the TFA-folder and hereby overwrite older files with the same name.
2.4
Deinstallation
The complete deinstallation
is simple: To that
- one opens the Windows-Explorer e.g. with the key
combination „<Windows> + <E>",
- chooses the folder into which the installation was
performed,
- clicks with the right mouse button on it and
chooses the command “delete".
3
Start of program
The program is started by a
double-click with the left mouse button onto the file „TFA.exe". To that one
- opens the Windows-Explorer e.g. with the key
combination „<Windows> + <E>",
- selects the folder into which the installation
was performed,
- carries out a double-click with the left mouse
button on the file „TFA.exe ".
Notices for more convenience:
More convenient may be the
one-time setup of a link on the desktop. To this one
- opens the Windows-Explorer e.g. with the key
combination „<Windows> + <E>",
- selects the folder into which the installation
was performed,
- performs a right-click on the file „TFA.exe"
and chooses „create link” (or comparable).
- The new linking may then be pulled onto the
desktop with left mouse button.
Instead of the creation of a
linking one can stitch „TFA.exe" also onto the start menu. To that one
- opens the Windows-Explorer e.g. with the key
combination „<Windows> + <E>",
- selects the folder into which the installation
was performed,
- performs a right-click on the file „TFA.exe"
and choosees and „stitch to start menu” (or comparable).
One notices, however, that in case of a
deinstallation the convenience-steps are to be revoked manually (deleting
desktop-linking and/or to deleting program from start menu).
4
The TFA progam window
When starting the program the following program window is shown
according to the chosen view-options:
Figure 4‑1: The TFA programm window after program start
Opening e.g. the WAV-file „IND_TFA.Wav" (contained in scope of
delivery) with the command “open file”, one already obtains an analysis with
the representations of time domain (to the left or above), frequency domain
(above and/or to the left) and the time-frequency domain (to the right -
below):
Figure 4‑2: TFA after opening file „IND_TFA.Wav“, FFT-lenght:
1024
As with most Windows-programs there is:
·
The menu bar
·
Short-Keys for frequently used functions and commands
·
The work space, that contains the three
representations time domain, frequency domain and time-frequency domain
·
Next to that some measurement tools are to be seen
according to the chosen options.
These program elements shall be explained now. The beginning does „The
work space with the representations time domain, frequency domain and time-frequency
domain”, because it allocates the biggest area in the main window.
4.1
The
work space with the representations time domain, frequency domain and time-frequency
domain
The figure above shows already
the most important elements of the work space, the three representations:
- Time domain
- Frequency domain
and
- Time-frequency
domain
4.1.1
The representation „Time domain“
It corresponds to an oscillogram of a time signal. Its axes are
correspondingly scaled with „time” and „amplitude". This representation
type is included in many products for signal analysis and does not contain any
special features. The graphic can be arranged to the left, as shown in the
figure above, or arranged in the upper working area, cf. section 4.3.5.
4.1.2
The representation „Frequency domain“
This representation shows the
spectrum of the time interval, whose centre corresponds to the temporal
coordinate of the mouse pointer in the time-frequency representation, see
below. The transformation parameters, therefore
- transformation
method
- spectral- and temporal resolution
- window functions
are explained in section 4.3.15 „Spektralanalysis settings„. The graphic can be arranged upside, as shown in the
figure above, or in the left of the work space, cf. section 4.3.5.
4.1.3
The
representation „Time-frequency domain “
One can imagine this
representation, known also as a spectrogram or in case of voice signals
as sonagramm, as a common view of the frequency domain representations
of all shown points in time, and that in a single graphic. The in this
way necessary third coordinate could be obtained by changeover from the
two-dimensional to a cube. However experiments show, that shadowing effects may
hide signal components easily.
Most superior is the coloured
presentation of the third coordinate to which the energy is assigned. The way
energy and colour are associated is handled in section 4.2.2.4.
The graphic is always placed
below/to the left in the work space, however, the axis meaning conforms to the
arrangement of the other two graphics because bordering axes are common.
Usefull
note:
A double-mouse-click in this
representation initiates the storage of the spectral line vector (dB-scaled,
txt-format) for the point of time according to the mouse position. The
localization of the txt-file is the TFA
working dircectory. Point of time and the frequency resolution form the file
name.
4.1.4
Selection
and sizes of the representations
In Figure 4-2 a proposal for the sizes of the three representations
is given. For the benefit of a certain representation it may be sometimes
better to draw a graphic in a smaller way or completely to renounce it.
That is simply possible
through mouse-drawing of the window boundaries. As soon as the mouse pointer is
in the area of a window boundary, the typical mouse pointer symbol indicates
the readiness to size the figure. The following two figures give examples:
Figure 4‑3: TFA with enlarged time-frequency representation
Figure 4‑4: TFA with enlarged time representation
4.2
The
menu bar
The menu bar includes the points
- File
- View
- Options
- Help
The next sections pay attention to them.
4.2.1
File
It is selectable:
- Open…
- Export
- Close
4.2.1.1 Open
TFA can handle six file formats:
- WAV-Format,
16 Bit PCM, 1 channel (mono) und 2 channel (complex)
- WAV-Format,
24 Bit PCM, 1 channel (mono) und 2 channel (complex)
- WAV-Format,
32 Bit PCM, 1 Kanal (mono) und 2 channel (complex)
- WAV-Format,
32 Bit FLOAT, 1 channel (mono) und 2 channel (complex)
- TFA-Format, 32 Bit, 1 Kanal (mono,
reell-wertig) und 2 channel
(complex)
- TXT-Format, Textfile
4.2.1.1.1 WAV-Format, 16 Bit, 1 channel (mono)
PCM-16-Bit is the mostly used
format. Normally a signal recording will subsist as a one-channel real valued
file, therefore a usual recording in mono.
4.2.1.1.2 WAV-Format, 16 Bit, 2 channell (complex)
TFA can also handle
complex valued signal files. Such can arise e.g. at the output of a digital
down converter (DDC) and contain a real part (Re) and an imaginary part (Im).
The sample sequence within the file is (Re), (Im), (Re), (Im).... . For this
two-channel file format the use of the Stereo-WAV-format has prevailed. Instead
of the left-/right-Information the two channels are interpreted as real part
and imaginary part. TFA cannot be
used for processing stereo files.
Notice: In order to be
able to process this file format still more precisely, at first a sampling rate
doubling is performed in TFA. Through that the measurement properties
improve, but the indicated sample numbers have the double valuation in the
comparison with the file. Time and frequency reference is not affected by that
of course.
4.2.1.1.3 WAV-Format, PCM, 24 Bit and 32 Bit,
1 channel and 2 channels
These formats are similar to
those described in the two sections before. The difference is the use of 3 and
4 Bytes per sample to achieve a higher dynamic range.
4.2.1.1.4 WAV-Format, FLOAT, 32 Bit, 1 Kanal bzw. 2 Kanäle
This format stores each
sample as a floating-point-value instead of PCM.
4.2.1.1.5 TFA-Format, 32 Bit, 1 channel (real)
This is a TFA-format which supports the
following:
- Samples are
stored in the format 32-bit-Float instead of having
samples as 16-bit integer values. Through that in case of the signal-export
and/or signal-import the otherwise always occurring conversion loss is
dropped.
- The sampling
rate is also stored as 32-bit-Floating point, to support very slow
processes, (e.g. earth science) and also very fast ones (e.g. radio
technology).
- The format includes a timestamp, so that the time-reference does not get lost due to
signal extractions.
The layout of the
TFA-file-format is given in chapter 9.1.
4.2.1.1.6 TFA-Format, 32 Bit, 2 channel
(complex)
The same explanations are valid
as in the section before.
4.2.1.1.7 TXT-Format,
Textfile
Sample sequences are often given
as text files. The values are written as plain text. They may represent integer
numbers and/or floating point (real) ones. The values are separated by
so-called „White-Space-Characters", e.g. by blanks or „returns”.
A textfile begins with 4
Info-values, followed by the samples:
- Info-value: Time of the first sample (start time)
- Info-value: Unit of the start time
- Info-value: Samplingrate or periodic time between
samples
- Info-value: Unit of the samplingrate ort the
periodic time.
Valid
units consist of an optional
multiplier and the unit. Multipliers my be:
- n 10 e -9
- u 10 e -6
- m 10 e -3
- k 10 e +3
- M 10 e +6
- G 10 e +9
Valid
units are:
- s Seconds,
used for the start time
- yr Year,
used for the start time or the sampling rate when given as sampling
interval
- Hz Hertz,
used for the sampling rate
Exapmle: A series of
measurement from earth science begins in the year 1958, wheras the time between
two measurements is 0.0833333 years. The textfile would begin then als
follows::
1958.0 yr
0.08333333
yr
315.56
315.56
315.56
317.29
317.34
316.52
315.69
………
Many other software products
can export in the TXT-format so that thus an interface exists.
Notice: Text files offer the
possibility to leave the restrictions of the WAV-format. If, however, it is
supposed to be exported from TFA in WAV-files, attention is to be paid
to not infringing the 16-, 24-, 32-bit value range because WAV-files are
overdriven then. It is also to be noted, that the WAV-Format only allows
sampling rates given as integers. The above described TFA-files are not
affected by that.
4.2.1.2 Export (complex) respectively Export
(real)
As referred in the section
above, TFA can handle real- and complex-valued signals. Not necessarily
for TFA, however for other applications it can be helpful to be able to
convert the two formats among each other.
With this command one can
render a loaded real-valued signal file into a complex-valued one and vice
versa. In the first case that means a frequency band shift around the amount of
half the sampling frequency and subsequent halving the sampling rate. In the
second case the sampling frequency is doubled after the frequency shift. Of
course the total bit rate remains unaffected, because also the number of
channels is changed.
4.2.1.3 Close
This command closes TFA.
Program settings like e.g. FFT-lengths and other transformation parameters are
stored and are maintained for the next program restart. As customary, TFA
can also be closed through a click onto the red cross 
in the program header.
4.2.2
View
It is selectable
- XY-Marker
- XY-Grid
- Uncertainty area
- Level key
- Mouse coodinates
- Progress
If the entries are marked (tick), the corresponding elements are visible
in the program window.
4.2.2.1 XY-Marker
The XY-marker is some
cross-hairs whose point of intersection is coupled to the mouse pointer
position in the time-frequency domain.
Important notice:
Sometimes this coupling is
unwanted because e.g. for documentation purposes the XY marker shall stay while
the mouse pointer leaves the representation. For a dissociation of the mouse
pointer and the XY marker one presses the key „STRG", sometimes also
called „CONTR". For the duration of the keystroke the coupling is
canceled. In this case it is important that TFA is the currently active window
that accepts key activations.
4.2.2.2 XY-Grid
The XY grid is a net of
auxiliary lines in the time-frequency representation. The two other
representations (time domain and frequency domain) are not affected by this option.
4.2.2.3 Uncertainty
area
According to the uncertainty
relation in the communication engineering and time-frequency analysis a precise
localization in time direction stands towards a simultaneously precise
localization in frequency direction. Both quantities can not be given
simultaneously exactly. So there is one uncertainty of the measurement in time
direction and one in frequency direction. The product of the two uncertainties
stretches the uncertainty area in the time-frequency domain. A decrease of the
area is desirable of course, it can be obtained by the built-in
DXP-transformation methods.
In order to gain a survey of the
uncertainty associated with the transformation settings quickly, TFA is
endowed with a face indication. On one hand it indicates the total area in
dependence of the scaling settings. And on the other hand it indicates the
uncertainty distribution that mainly turns out through the size of the time signal
interval coming in into the computation.
At the program start or after switching on this option the uncertainty area is
arranged for instance in the middle of the time-frequency domain and
magenta-coloured. It can be displaced, however, to every arbitrary point of the
program window with the mouse through the left mouse button. In Figure 4-2 the uncertainty area
is to be seen left of the
spectrum (above) respectively above the time representation (left hand). The
denomination „uncertainty" points at an uncertainty area with the form of
a point. This point appears very concentrated, because the spectrogram shows a
relatively big signal section both in frequency- and also in time direction.
A display-zoom with the
values:
- Time domain: 0.35
s to 1.0 s
- Frequency range: 50
Hz to 500 Hz
increases the detail level
and in this way also the „illustration" of the uncertainty area, as
following figure shows.
The uncertainty area is maybe
a little difficult to be found in the coloured environment of the
time-frequency domain.
Assistance: It lies a little
bit right above the XY Marker cross-hairs'.
Figure 4‑5: Uncertainty area at transformation FFT, FFT-length: 1024
Caution: The physical
uncertainty area is not increased due to that zoom, only its representation.
Increasing the FFT-length to
e.g. the value 4096 yields to the following spectrogram:
Figure 4‑6: Uncertainty area at transformation FFT, FFT-length: 4096
The uncertainty area
has grown around the factor 4
in direction of the time axis because a four times bigger time interval comes
into the calculation. In frequency direction on the other hand the size was
reduced around the factor 4.
The area itself is not
changed through enlargement or reduction of the FFT length, only the length
distribution. One can recognize, however, at least optically by means of the
two representations, that the indicated uncertainty area agrees in fact with
the uncertainty of the spectrogram.
What happens now with the
uncertainty area due to a selection of the transformation DXP-I?
Figure 4‑7: Uncertainty area at DXP-I, resolution: 4096, time-window: 256 Samples
Also here the uncertainty
area is
is arranged a little
right-above the XY-Marker cross-hairs. One recognizes in agreement with the
spectrogram, that
- the small magenta-coloured circle-similar face is
just as extensive now in frequency direction, see Figure
4-6, because in both cases the FFT resolution is
4096,
- however the temporal extension is reduced around
the factor 8, what is associated with the reduction of the time window
interval of 4096 onto 256 samples.
Nevertheless please try it
out later yourselves as soon as the remaining control elements were also described
here!
4.2.2.4 Level key
A spectrogram, therefore a
time-frequency analysis is a tridimensional representation. The third dimension
represents the energy which is colour coded. The level key, to be seen in the
right middle of the spectrogram in the figures above, is an assignment table
that relates colours corresponding to the energy steps.
Just like the representation
of the uncertainty area the level key legend can be moved to any place of the
program window with the mouse pointer by means of the left mouse button.
The setup of the level
colours is freely possible, see section 4.2.3.1 “Colours”.
4.2.2.5 Mouse
coordinates
If one moves the mouse
pointer over the signal presentations, an information sheet indicates the
signal quantities linked with the mouse coordinates. In case of the
time-frequency representation that are:
- Time
- Amplitude
- Frequency
- Energy
The mouse coordinate
information sheet can be moved with the mouse pointer by means of the left
mouse button anywhere in the area of the program window as well.
4.2.2.6 Progress
Depending on the performance
of the used computer some arithmetic operations may last a little longer. An
optical control for the process progress is a turning atom which appears at the
contact-place of the three signal presentations[2].
4.2.3
Options
TFA offers some options to an individual setup of the program:
- Colours
- Working directory
- Language/Sprache
- Settings
- Prog.-Start
with FFT
- DC-Offset-correction
- 1.0-Scaling
The settings are stored during the closing of the program.
4.2.3.1 Colours
With this command the
operation- and settings-window „Functions and parameters" is opened
directly with the tab "Settings":
Figure 4‑8: Operation window „Functions and parameters->Settings
“
In the upper half the colours of
- the level
legend
- many program
elements
can be configured.
4.2.3.1.1 Level-Colour-Assiociation
The first field „number of
level-colour-steps" is used for the setting of the colour resolution
of the energy in the time-frequency representation. The list „dB-levels"
contains as many dB-entries. Every level is separately eligible and may be
assigned a colour with the colour dialog (key 
). With the key “Default” the level-colour-association
happens automatically in an intuitive color course:
- High energy: Red
- …
- Low energy: Blue,
black
4.2.3.1.2 Colour
settings
The selection field „Colour
settings" lists all control elements that colour can be changed. Every
control element is separately eligible and may be assigned a colour with the
colour dialog (key 
). With the key “Default” the colour assignment happens
automatically in the form of a colour proposal.
4.2.3.2 Working directory
There are functions in TFA
which write intermediate files onto the hard disk. With this option one can
pre-set the disk drive location.
4.2.3.3 /Language/
Sprache
TFA is written in the
national languages of German and English. With this option one chooses the
language.
4.2.3.4 Settings
With this command the
operation- and settings-window „Functions and parameters" is opened
directly with the tab "Settings", see Figure 4-8.
The settings contain graphic
and transformation properties defined by the user.
Several sets of settings can
be stored and loaded with the left two keys in the lower window half. With the
right key 
the factory settings can be reconstructed.
4.2.3.5 Prog.-Start
with FFT
During the termination of TFA
all settings are stored and loaded at a renewed start of program again. In the
case of the spectral transformation setting „DXP-I" that can be
disadvantageous because - maybe unintentional - after opening of a signal file
the slower DXP-transformation is immediately performed. This can be prohibited
through marking of this option.
4.2.3.6 DC-Offset-Correction
If this option is checked a
DC-offset will be removed while opening
a signal file.
4.2.3.7 1.0-Skalierung
If this option is checked
dependend on the file format the signals full scale is scaled to the value 1.0 while opening a signal file. So the
scale is not bounded to the file format.
Example: In case of a 16-Bit-PCM-Wav-file a sample with an amplitude of
32767 will be scaled to 1.0.
4.2.4
Help
TFA offers two possibilities for assistance:
- Documentation - This command indicates
this file.
- Info - Here you find the present program
version and reach
4.3
The short-keys
A basic principle during the
development of the TFA user interface is the use of the
screen area as efficient as possible. Therefore most control elements and input
fields are quartered in a separate window „Functions and parameters".
Saving place the short-keys offer access to the most important control elements
and if necessary open the window „Functions and parameters" for
advanced setting functions. Short-keys are available for following functions:
- Open
- Documentation
- Info
- Presentation
continuous / discrete
- Orientation
- Automatic scaling
- Area selection
- Vertical markers
- Horizontal markers
- Vertical Harmonic
marker
- Horizontal Harmonic marker
- Advanced XY-Marker functions
- „Zoom" -in and
-out
- Advanced Zoom / range functions
- Spectrum analysis settings
- Play / export
- DDC - Digital Down
Converter
- Graphic-export
- Status control
The functions are explained
in the following.
4.3.1
Open
This command opens a signal
file as described in section 4.2.1.1.
4.3.2
Documentation
The command indicates this document in the HTML-format.
4.3.3
Info
Here you find the present
program version and reach
4.3.4
Presentation continuous / discrete
In Digital Signal Processing
the number of a sample is associated with the its sampling time [s] by means of
the sampling frequency. Similar is valid for the number of a spectrum line and
the represented frequency [Hz]. With this command the presentation may be switched
between time [s] respectively frequency [Hz] and time sample number
respectively spectrum line number. One can e.g. purposefully find a wanted
sample or indicate values in its physical context.
4.3.5
Orientation
This command exchanges time
and frequency axis. Figure 4-7 would then turn as follows:
Figure
4‑9: Exchange of Orientation
4.3.6
Automatic Scaling
According to chosen signal
section the level distribution can be very different. On the one hand this
function adjusts the energy scaling of the time-frequency domain and the
spectral representation and on the other hand the amplitude scaling so, that
the diagrams are „well gained".
It is often worthwhile, to
call this function also e.g. after an alternation of
- the transformation method or its
parameters since due to the different uncertainty properties the existent
energy is distributed over a larger or smaller area or
- the signal selection.
The in the following
described control elements lie in the field
4.3.7 Area
selection
.
For many TFA-functions it is
necessary to be able to select a certain signal range. The easiest possibility
for the selection of a signal range is maybe the drawing of a rectangle with
the mouse, similar like it is known from graphic arts software.
In order to activate this
function select mode, the area selection key is to be pressed. After that
selection rectangles can be stretched in all representations as following
example shows.
Figure 4‑10: Area selection in the time-frequency domain
Such an area one can then
e.g. enlarge (zoom), extract, export et cetera.
4.3.8
Vertical markers
Vertical markers are vertical
auxiliary lines in diagrams that can be positioned there with the mouse. After
pressing the key “Vertical markers” there are 2 markers (1’ and 2’) available
in every representation.
The marker positions appear
in a value table below the short-key-bar e.g. as follows:
Figure 4‑11: Value table for vertical markers
Apart from the marker
positions also the column (2’ -1’) is to be seen. It shows the distance of the
two markers.
The marker position
may be adjusted with the mouse or placed exactly via entry of a wanted
numerical value into the white fields.
Notice: The activation of
the vertical markers deactivates other vertical markers and the area selection,
see below.
4.3.9
Horizontal markers
Horizontal markers are
horizontal auxiliary lines in diagrams that can be positioned there with the
mouse. After pressing the key „Horizontal markers” there are 2 markers (1’ and
2’) available in every representation.
The marker positions appear
in a value table below the short-key-bar comparable to Figure 4‑11: "Value
table for vertical markers”, see above.
Also here is valid:
Apart from the marker
positions also the column (2’ -1’) is to be seen. It shows the distance of the
two markers.
The marker position
may be adjusted with the mouse or placed exactly via entry of a wanted
numerical value into the white fields.
Notice: The activation of
the horizontal markers deactivates other horizontal markers and the area
selection, see below.
4.3.10
Vertikal harmonic marker
A Harmonic-marker consists of
a band of markers that are characterized by two quantities:
- Marker start - the position of the
first marker of a band
- Distance – Distance of two neighbouring
markers
Harmonic markers are used in
order to be able to measure cyclical processes over several cycles.
An example is the measurement
of a digital data stream in the case of which the bit length is constant.
Figure 4‑12: Measurement exampe with „Vertical harmonic markers“
The marker positions appear
in a value table below the short-key-bar comparably Figure 4‑11: „Value table for vertical markers", see above.
One reads off that the
temporal bit-distance of the frequency shift keying is 4,16 ms, which
corresponds to a modulation rate of about 240 Bd. By the way: The example shows
a FSK radio transmission method, where the information transmission reclines in
the keying of two frequencies.
Notice: