TFA-Joint Time-frequency analysis

JTFA - Joint Time Frequency Analysis

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.

TFA-Spectrogram of a speechsample: Resolution 4096 Lines computed from 512 samples

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 therestrictions 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),
do 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. Unfortunately this has, however, its price: The analysis speed can lie considerably under that of conventional procedures. That is not a product lack, but results from the extensive computations which are necessary for obtaining the analysis quality.

TFA - Time-Frequency Analysis


Test and purchase TFA

TFA is written in german and english (selectable).

TFA runs on Windows-PCs and Apple MACs.

The Windows-PC-version is available at the german IND-shop:
Please notice that there is a sale or return within 14 days - a money-back guarantee.
Also note that new customers please may pay in advance.

The Apple-Mac-version "TFA - Time-Frequency Analysis" is available at your local Appe Store.
For example:
You can change the /de/ to your country code to access your Apple Store if the link is not forwarded.

Further information

Contact for any questions and a free of charge TFA-analysis of YOUR signal sample.
The german TFA site or for all things that are not presented in the english article yet.

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