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Unformatted text preview: Department of Electrical Engineering EE 308: Communication Systems (Spring 2009) Solutions to Class Test 2 07/02/2009 1. A signal x ( t ) = A m cos(2 πf m t ) is amplitude modulated with carrier A c cos(2 πf c t ). The maximum possible value of modulation index is - The minimum value of μ.x ( t ) should be greater than -1. Since the minimum value of x ( t ) is − A m , therefore, the maximum possible value of μ = 1 A m . 2. Let f ( t ) = rect ( t/T ). The bandwidth of the main lobe in the fourier transform of f ( t ) is - The fourier transform of f ( t ) is | T | sinc ( fT ). The bandwidth of its main lobe is 2 T . 3. integraltext ∞-∞ sinc 4 ( t ) dt =? The Fourier transform of sinc 2 ( t ) is Δ ( f 2 ) . Using Parseval’s theorem, integraldisplay ∞-∞ sinc 4 ( t ) dt = integraldisplay ∞-∞ Δ 2 parenleftbigg f 2 parenrightbigg df = 2 integraldisplay 1 (1 − f ) 2 df = 2 3 (1) 4. The Nyquist sampling frequency of the signal sinc (200 t ) + sinc (200 t ) 2 is - The fourier transform of | T | sinc ( tT ) is rect(f/T) which has a bandwidth of T 2 . The fourier transform of...
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- Spring '09
- Electrical Engineering