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f2000b - Spectrogram Analysis and Applications Overview The...

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Spectrogram Analysis and Applications Overview The frequency characteristics of nonstationary signals vary as a function of time. This requires Fourier analysis of these signals to be localized and time-dependent, resulting in analysis methods known as time- frequency distributions. One elementary time-frequency distribution based on the FFT is the short-time Fourier Transform (STFT). The STFT applied to speech is often called a speech spectrogram . Spectrograms are well suited to analyze speech signals with their time-varying narrowband features. In this project, you will: Calculat e spectrogra m s of frequency m odulat ed signals. Construct n arrowband and wideband sp ectrogra m s of sp e ech signals. Estimat e a sp e ech signal from a m odified STFT. Modify the tim e scale of a spe ech signal. The project zip file cont ains the audio files and MATLAB functions which you will ne ed for this proje To access the zip file, click on the link b elow where you found this file on the web site. Spectrogram Definition The sp ectrogra m of a signal x[n] is d efined a s: where ϖ [n] is the window used. The window will det er mine what portion of the signal is used for a n alysis and controls the frequency resolution of the spectrogra m. The para m et er n d enot es the reference position of the window on the signal. Let the window be of length N win and nonzero only in the interval 0 ≤ k ≤ (N win - 1) . The above equation reduces to: f200b
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Computing Spectrograms in MATLAB It is easy to construct spectrograms in M ATLAB since the STFT involves only windowing and the FFT. This project will require extensive use of the M ATLAB function spectrogram . It is suggested you take some time to fully understand the details of the spectrogram function. This can be done by typing help spectrogram at the M ATLAB prompt. For a more graphical presentation of the help (including figures) try doc spectrogram . A few important points about the spectrogram function for this project: Note that if the spectrogram is defined as it is in the previous section, the first column of the spectrogram generated by MATLAB is really , not X 0 ( ϖ ) . The spectrogram function with no output arguments will plot the results to the current figure. For real signals x[n] , the spectrogram function only calculates or plots a portion of the frequency components (from 0 to π ) since the remaining are “redundant”. How are they “redundant”? It is common in speech processing to use a “short” time window and to plot frequency on the y axis. When you have loaded the speech signals mentioned below, the command spectrogram(s1,hamming(256),’yaxis’) will produce a good example spectrogram plot. Please use the ‘yaxis’ parameter for all your figures.
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