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EE200_frequency_domain

EE200_frequency_domain - EE 200(Fall 2008 Lab 3 Frequency...

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EE 200 (Fall 2008) Lab 3 – Frequency Spectrum 1 Introduction The purpose of this lab is to learn to examine the frequency domain content of signals. The method used will be to plot the discrete Fourier series coefficients of finite signals. This lab is based on lab 7 in the lab manual that accompanies the textbook by Lee & Varaiya . 2 What you will learn Frequency domain representation is a powerful tool for examining signals and can be used to see aspects of the signal that are often not evident by looking at the time domain representation. In this lab you will construct some signals and then find the frequency domain representation of them. Once in the frequency domain some simple filtering will be done to bring out parts of the signal that could not be seen (or heard) due to noise. 3 Background Information and Notes A finite discrete-time signal with N samples has a discrete-time Fourier series expansion x ( n ) = A 0 + N/ 2 summationdisplay k =1 A k cos( 0 n + φ k ) where ω 0 = 2 π/N . A finite signal can be considered to be one cycle of a periodic signal with fundamental frequency ω 0 , in units of radians/sample, or 1 /N in Hertz. In this lab, we will assume N is always even, and we will plot the magnitude of each of the frequency components, | A 0 | , · · · , | A N/ 2 | for each of several signals, in order to gain intuition about the meaning of these coefficients. Notice that each | A k | gives the amplitude of the sinusoidal component of the signal at frequency 0 = k 2 π/N , which has units of radians/sample. In order to interpret these coefcients, you will probably want to convert these units to Hertz. If the sampling frequency is f s samples/second, then you can do the conversion as follows (see box on page 248 of the text): ( k 2 π/N )[radians / sample] f s [samples / second] 2 π [radians / cycle] = kf s /N [cycles / second] Thus, each | A k |
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