20091ee114_1_CA3_sol

# 20091ee114_1_CA3_sol - for ”sweep” shows energy...

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UCLA Dept. of Electrical Engineering EE 114, Winter 2009 Computer Assignment 3 - Solutions Abstract : This assignment focusses on the relationship between temporal and spectral resolu- tion during speech analysis. The eﬀect of window size during the calculation of FFTs is studied. Additionally, the assignment studies the use of time-frequency representations, or spectrograms, during speech processing. The eﬀect of analysis window length, as well as overlap length, is stud- ied. Speciﬁcally, we inspect the results of various parameters on the resolutions of harmonics and formants frequencies. The Eﬀect of Window Size : 1. For the male and female signals, the window lengths at which harmonics are no longer re- solved are determined to be approximately: L =90 samples for male L =50 samples for female These window lengths correspond to spectral resolutions (DFT-bin spacings) of: Δ F = Δ ωF s 2 π = 2 π L F s 2 π = 89 Hz for male Δ F = Δ ωF s 2 π = 2 π L F s 2 π = 160 Hz for female Spectrograms : 1. The spectrogram corresponding to ”tone” shows constant energy at 1000 Hz. The spectrogram
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Unformatted text preview: for ”sweep” shows energy sweeping from 0 Hz to 4000 Hz at a linear rate. The spectrogram for the ”noise” signal shows energy evenly spread with respect to frequency and time. 2. If L =256 and N OL =240, the length of the increment (”hop”) in samples is L hop =16 samples. This corresponds to: T hop = 16 samples × 1 F s = 2 ms . (1) The rate at which successive FFTs are calculated is determined as: F FFT = 1 T hop = L-N OL F s Hz . (2) 1. For long window lengths, the horizontal striations correspond to harmonics. 2. The vertical striations occur since short window lengths results in increased temporal resolu-tion. 3. The parameter set which can be considered best for estimating formant frequencies for the male sentence is (120,90). At these settings, harmonics are no longer resolved, and the shape of the spectral envelope is clear. 1...
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