20091ee114_1_PS1_Sol

# 20091ee114_1_PS1_Sol - UCLA Dept. of Electrical Engineering...

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UCLA Dept. of Electrical Engineering EE 114, Winter 2009 Problem Set 1 - Solutions 1. Let x a ( t ) be a continuous-time speech signal 50 ms in duration, that is sampled at F s = 16 kHz. We wish to perform spectral analysis using a radix-2 FFT, with spectral resolution of at least 20 Hz. What is the minimum length, N , of the FFT used? If the original signal was 75 ms in duration, would this aﬀect the design of your algorithm? If so, how? Answer: The minimum spectral resolution is given in continuous-domain frequency, Δ F min = 20 Hz. This corresponds to a discrete-domain frequency of: Δ ω min = 2 π Δ F min F s = 2 π (20) 16 , 000 = 0 . 0025 π (1) The spectral resolution provided by a N -point DFT is given by 2 π N . Thus: 2 π N 0 . 0025 π N 800 . (2) However, since a radix-2 FFT is used: N = 2 10 = 1024 . (3) A N = 1024 point FFT corresponds to a 65.63 ms segment of speech. Thus, if the original segment was 75 ms in duration, this would result in aliasing in the time domain. Instead, a

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## This note was uploaded on 05/10/2010 for the course EE EE114 taught by Professor Vanderschaar during the Spring '09 term at UCLA.

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20091ee114_1_PS1_Sol - UCLA Dept. of Electrical Engineering...

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