信号的时频分析-2.ppt

“Time-Frequency Analysis”Short-time Fourier transform 2011.4.28 Steps of time-frequency analysis Estimate the stationary of signal Decompose the signal Observe the time-frequency results Recover signal or model the signal Contents Introduction Time-dependent processing The short-time Fourier transform Applications of the short-time Fourier transform Sometimes one is interested in the short-time energy over a specific frequency band rather than that of the entire signal. In this case, the signal is first bandpass filtered, then the short-time energy of the filter output is computed. This method is the best one when w0[n] is an IIR filter because the short-time energy can be evaluated recursively. On the other hand, if w0[n] is of finite duration, there exists an alternative method for computing the short-time energy. Rn[0] = En if the same window w[n] is used in both expressions. The effect of the window is to “smear” the signal spectrum X (f ), so that the frequency resolution of the STFT is limited by the bandwidth of the window ΔW . Specifically, the longer the window, the smaller its bandwidth, and the finer the frequency resolution. the harmonics of the 100 Hz fundamental frequency are resolved with the 40-ms window, but not with the 10-ms window. Window =1 Window 2, linear chirp 3, EEG: eyes-open and eyes-closed 4, sleep ECOG 6; matlab example fs = 10000; t = 0:1/fs:2; x = vco(sawtooth(2*pi*t,.75),[0.1 0.4]*fs,fs); %Y = VCO(X,[Fmin Fmax],Fs) creates a signal which oscillates at a frequency determined by the input vector X. scales the frequency modulation range so that -1 and 1 values of X yield oscillations of Fmin and Fmax Hertz respectively. spectrogram(x,kaiser(256,5),220,512,fs,yaxis) %Spectrogram using a Short-Time Fourier Transform (STFT). Applications of the short-time Fourier transform 1, STFT 5, task-related EEG Time/msec Frequency/Hz 4 3 2 1 0 dB 1 2 3 4 Visual Search Visual Pop-out * * * Introduction Methods for two broad classes of signal