# hw2 - Homework 2 ECE 220 Due 1 A signal x(t has the...

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Homework 2 ECE 220 Due February 17, 2005 1. A signal x ( t ) has the two-sided spectrum representation shown in Figure 1. (a) Write an equation for x ( t ) as a sum of cosines. (b) Is x ( t ) a periodic signal? If so, determine its fundamental period and its fundamental frequency. (c) Explain why ”negative” frequencies are needed in the spectrum. CD: Spectrum Complex Exponentials; Period. CD: Spectrum Sinusoids; Fundamental Frequency and Period. CD: Spectrum Sinusoids; Period. 2. Consider the signal x ( t ) = 7 + 10 cos(2 π 500 t ) + 6 cos(2 π 600 t ) (a) Using Euler’s relation, the signal x ( t ) defined above can be expressed as a sum of complex expo- nential signals using the finite Fourier synthesis summation (Equation 3.30 in text). Determine values for N and all complex amplitudes a k (You should not need to evaluate any integrals). (b) Is the signal x ( t ) periodic? If so, what is the fundamental period? (c) Plot the spectrum of this signal versus f in Hz. CD: ”Determine Fourier Series for a Sum of Cosine Signals” 3. Read through and complete Problem 3.14 from your text.

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• Spring '05
• JOHNSON
• Fourier Series, spectrum, Fourier series coefficients, two-sided spectrum representation

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