Lab_15__Fourier_Series_joshdean_LAB15_joshdean

Lab_15__Fourier_Series_joshdean_LAB15_joshdean - Joshua...

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Joshua Dean Lab 15: Fourier Series March 28, 2011 The George Washington University School of Engineering and Applied Science ECE 3220 Digital Signal Processing Lab Section 30 GTA: Damon Conover Total Grade = 90/10 0 [10] Plot magnitude and phase of H(jw) [10 points] [15] Plot and compare x(t) and the approximation of x(t) [20 points] [30] Three-panel plot of spectrum of x3(t), magnitude of H(jw), and spectrum of y3(t) [30 points] [10] Plot y10(t) [10 points] [10] Determine dc value and first coefficient of input signal [10 points] [5] Solve for R and C [10 points] [10] Plot output signal with correct DC and ripple voltage [10 points] Introduction As the lab report states “goal of the laboratory project is to show that Fourier Series analysis is a powerful method for predicting the response of a system when the input is a periodic signal.” [1] MATLAB uses MAPLE to perform symbolic computations, for example:
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derivatives and integrals. The utilization of MAPLE for this lab is crucial, due to the high amount of symbolic computation required. The Fourier Series of continuous time signals were analyzed by integration. This lab also analyzes a power supply circuit through the use of symbolic representations. The circuit itself was an AC-DC voltage converter using a full wave rectifier (formed from a diode bridge), and a RC low-pass filter. Laboratory Analysis of a Power Supply Circuit Figure - Power Supply circuit: AC to DC voltage converter The analysis of the above circuit consisted of “finding the Fourier Series for the input x(t); multiplying by the frequency response of the low pass filter; and then evaluating the size of the Fourier coefficients for the output signal.” [1] As seen from the circuit in Figure 1, the output of the rectifier becomes the input of the RC circuit, which then becomes y (t). The relationship between input and output voltages can be seen from the following equation: Equation 5.1 Fourier Analysis of the Full-Wave Rectifier The first assumption made is that the input power line voltage is .
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The lab asks for a function to plot the magnitude and phase of the frequency response over the range -2π(400)≤ ω ≤ 2π(400) [without the use of premade MATLAB functions], and then to test the function by plotting R = 33000 ohms and C = 5 × 10−6 farads [see APPENDIX A] . The magnitude is the absolute values of the frequency response, while the phase is the angle of the
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This note was uploaded on 11/14/2011 for the course ECE 3220 taught by Professor Conover during the Fall '11 term at GWU.

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Lab_15__Fourier_Series_joshdean_LAB15_joshdean - Joshua...

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