<p>Joint Time Frequency Analysis is like a shorter Fast Fourier Transform where wavelet packets are analyzed and transformed into quantitative displays. By applying a form of JTFA, you can identify not only the frequency content of a signal, but also how
    that content evolves over time. Thus, JTFA is great at showing changes over time (we get to see “what” is happening “when.”</p>
<p>Joint-Time Frequency-Analysis (JTFA) is used for real-time EEG biofeedback and is used to compute statistical Z scores in real-time. JTFA relies on complex demodulation, which is an analytic technique that multiples a time series by a sine wave and a
    cosine wave and then applies a low pass filter (Granger et al, 1964; Otnes and Enochson, 1977). JTFA computes instantaneous power, instantaneous phase differences, and instantanous coherences. Unlike the Fourier transform,&nbsp; which depends on windowing
    and integration over an interval of time, JTFA complex demodulation computes and creates an instantaneous Z score within subject variance of instantaneous electrical activity as well as the between subject variance for subjects of a given age. The
    summation of instantaneous Z scores is Gaussian distributed and has high crossvalidation (Thatcher et al, 1987; 2007), however, the individual time point by time point Z score is always smaller than the summation due to within subject variance.</p>
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<p style="text-align: center;"><iframe src="https://player.vimeo.com/video/408145806" width="640" height="399" frameborder="0" allow="autoplay; fullscreen" allowfullscreen=""></iframe></p>
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<p style="text-align: center;"><img src="@@PLUGINFILE@@/spectrogram-eeg.png" alt="A colorful spectrogram showing, over the course of time, what frequencies and what amplitudes are being created in the raw EEG" width="881" height="403" class="img-responsive atto_image_button_text-bottom"><br></p>
<p style="text-align: center;">A colorful spectrogram showing, over the course of time, what <br>frequencies and what amplitudes are being created in the raw EEG<br></p>
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<p style="text-align: center;"><img src="@@PLUGINFILE@@/jtf-neuroguide.png" alt="Joint Time Frequency Analysis of Head Maps in Neuroguide" width="586" height="592" class="img-responsive atto_image_button_text-bottom"><br></p>
<p style="text-align: center;">Joint Time Frequency Analysis of Head Maps in Neuroguide<br></p>
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