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# pcshw5 - analytically(and justify any assumptions 4 Pulse...

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THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College of Engineering Department of Electrical and Computer Engineering 332:322 Principles of Communications Systems Spring 2004 Problem Set 5 Reading: Haykin 3.1–3.4 1. Nyquist 101: Specify the Nqyusit rate and Nyquist interval for each of the following signals. Note that sinc ( x ) sin( πx ) πx . (a) g ( t ) = sinc (200 t ) (b) g ( t ) = sinc 2 (200 t ) (c) g ( t ) = sinc (200 t ) + sinc 2 (200 t ) 2. Nyquist 102: Suppose we have samples of a signal a k = g ( k Δ) where Δ is shorter than the Nyquist interval for the bandlimited function g ( t ) . Derive an explicit time-domain expres- sion for how we recover the function g ( t ) from the samples { a k } . 3. Nyquist Grad School: Does the Nyquist Sampling Theorem apply to strictly time limited signals? If not why not? If so, why? This problem is a bit subtle so think carefully and
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Unformatted text preview: analytically (and justify any assumptions). 4. Pulse Modulation (a) What is Pulse Amplitude Modulation? Provide a pictorial example. (b) What is Pulse Position Modulation? Provide a pictorial example. (c) What is Pulse Frequency Modulation? Provide a pictorial example. (d) What is Pulse Width Modulation? Provide a pictorial example. (e) Consider a full wave recti±ed AM signal r ( t ) = m ( t ) cos 2 πf c t where we assume m ( t ) ≥ ∀ t . Assuming the highest frequency content of m ( t ) is much less than f c , can r ( t ) be considered the approximate result of a pulse modulation method applied to m ( t ) ? If so, which one? 5. Problem 3.5 in Haykin 1...
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• Spring '08
• Rose
• Pulse-width modulation, PULSE AMPLITUDE MODULATION, Nyquist–Shannon sampling theorem, pulse position modulation, pictorial example

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