Lab+04 - D ISCRETE-T IME S YSTEMS AND C ONVOLUTION 4...

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Unformatted text preview: D ISCRETE-T IME S YSTEMS AND C ONVOLUTION 4 Electrical Engineering 20N Department of Electrical Engineering and Computer Sciences University of California, Berkeley HSIN-I LIU, JONATHAN KOTKER, HOWARD LEI, AND BABAK AYAZIFAR 1 Introduction In this lab, we will explore discrete-time convolution and its various properties, in order to lay a better foundation for material to be presented later in the course. Convolution is an ubiquitous operation in signal processing, not least because it provides an elegant way to represent linear, time-invariant systems. The convolution of two signals x and y , in discrete-time , is defined as CONVOLUTION ( x * y )( n ) = X k =- x ( k ) y ( n- k ) = X k =- y ( k ) x ( n- k ) . In the case of LTI systems, the output signal of a system, y ( n ) , can be determined merely by convolving the input signal x ( n ) with the impulse response h ( n ) of that system: y ( n ) = ( x * h )( n ) . Furthermore, as you shall see later in Fourier analysis, convolution in the time domain translates directly into multiplication in the frequency domain. In this lab session, we will try several different approaches of implementing convolution in LabVIEW . Finally, we will see our first special-purpose discrete-time system, known as a discrete-time low-pass filter. We will analyze its behavior in the frequency domain and discover where it gets its name. 1.1 Lab Goals Explore the properties of discrete-time convolution. Implement discrete-time convolution in LabVIEW through different methods. Implement basic discrete-time filters in LabVIEW in both time and frequency domains. 1 1.2 Checkoff Points 2. Pre-Lab Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. LTI Systems and Impulse Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Echo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Flip-and-Shift Method (Using the Toolkit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (20%) 4. Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Submission Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Submission Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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Lab+04 - D ISCRETE-T IME S YSTEMS AND C ONVOLUTION 4...

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