{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps6 - 6.450 Principles of Digital Communication MIT Fall...

This preview shows pages 1–2. Sign up to view the full content.

6.450 Principles of Digital Communication Wednesday, October 9, 2002 MIT, Fall 2002 Handout #23 Due: Wednesday, October 16, 2002 Problem Set 6 Problem 6.1 (a) Show that for any T > 0 the set of functions { ψ m,k ( t ) = e 2 πimt/T sinc( t - kT T ) } is an orthogonal set. Hint: Show that the Fourier transforms of each of these functions are orthogonal to each other; review the argument used for the T - spaced truncated sinusoids. (b) Derive the energy equation, Eq. (13) in Lecture 9. Problem 6.2 The following exercise is designed to illustrate the sampling of an ap- proximately baseband waveform. To avoid messy computation, we look at a waveform baseband limited to 3/2 which is sampled at rate 1 ( i.e. , sampled at only 1/3 the rate that it should be sampled at). In particular, let u ( t ) = sinc(3 t ). (a) Sketch ˆ u ( f ). Sketch the function ˆ v m ( f ) = rect( f - m ) for each integer m such that v m ( f ) 6 = 0. Note that ˆ u ( f ) = m ˆ v m ( f ). (b) Sketch the inverse transforms v m ( t ) (real and imaginary part if complex).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

ps6 - 6.450 Principles of Digital Communication MIT Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online