SIGNAL SPACE

SIGNAL SPACE

1. INTRODUCTION

   • SIGNAL
     • ANALOG
       • CONTINUOUS
       • TIME PERIOD
       • Digital Communication System
     • DIGITAL
       • DISCRETE
       • SEQUENCE OF BITS
       • Represented as a Linear Combination of a set of Orthonormal Waveforms

2. SIGNAL THEORY

   • INNER PRODUCT
     • ORTHONORMAL SET
       • COMPLETE
     • COEFFICIENTS
       • Coordinates of vector with respect to the orthonormal Basis
       • UNIFORMLY SAMPLING in frequency domain
   • ENERGY
     • FINITE
   • DISTANCES
   • Using Orthonormal Expansions we can represent
   • DEGREES OF FREEDOM

3. TIME-LIMITED SIGNALS

   • FOURIER TRANSFORM
     • DIRAC DELTA FUNCTION
     • LINEARITY
     • INVERTIBILITY
     • ENERGY LIMITED
     • Cost of losing information from finding Orhonormal Expansions
   • Information received in few miliseconds

4. FREQUENCY-LIMITED SIGNALS

   • Narrow Frequency Band

5. SAMPLING FUNCTIONS

   • ORTHONORMALITY
   • An energy-limited signal x(t) frequency limited to W Hz can be perfectly reconstructed from samples
     • Nyquist sampling
   • Degrees of Freedom
     • Real-Valued Signals
       • 2WT+1
       • WT+1 (WT) (even)
     • Complex-Valued Signals
       • 4WT+2

6. COMMUNICATION CHANNEL MODELS

   • (AWGN)
     • Z(t) zero-mean White Gaussian Noise
       • Joint Probability Distribution
     • MUTUAL INFORMATION
     • Discrete-Time AWGN Channel

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