Communication Signal Processing Flashcards
communication system
includes source, channel, and receiver
- this combination is called a link
- Purpose is to transmit set of dat, {I}, from a source, over a channel, to a receiver
- {I} is typically in the form of electric signals controlled by sender
Frequency multiplexing
sending two or more signals over same channel using different frequency bands
- also called frequency-division multiplexing (FDM)
- used by TV, radio stations, and so on
- guard slot: a frequency range left unused between the used frequencies to prevent overlap of signals
- TV stations broadcast video and audio on separate carriers.
- Stereo radio is broadcast with sum and difference channels
- -> monaural receiver uses only sum
- -> stereo receiver reconstructs left and right channels
communication channel
any physical medium through which a signal is transmitted, such as
- copper wire
- fiber optic cable
- air
simplex channel: can transmit in one direction only
half-duplex channel: can transmit in either direction but not simultaneously
full-duplex channel: can transmit in both directions at once (usually combines two simplex channels)
Fourier analysis
can be used to express a complicated function in terms of less complicated sine and cosine waves
- Any periodic waveform can be expressed as the sum of an infinite series of sinusoidal waveforms (a Fourier series)
- The process of finding this series of sinusoidal terms is Fourier analysis
- Many Fourier series converge rapidly, so finite number of terms often gives a close enough approximation for practical purposes
Fourier transform
- changes a function of time, f(t) to a function of frequency F(w)
- allows spectral content of a waveform to be analyzed in frequency domain (that is as equivalent content of sine and cosine waves)
The waveform may be periodic or nonperiodic
- -> If periodic, spectral content will be lines in the frequency domain
- -> If nonperiodic, spectral content will be a distribution in the frequency domain
Convolution
mathematical operation the can be used to model or predict results of passing a signal through a device
- allows determination of response of a linear system to any input based on the system’s impulse response
- can be performed on both continuous and discrete time signals
impulse response h(t)
the response of a linear time invariant system with transfer function H(s) to an impulse
- once h(t) is known, the response, y(t), to any input signal, x(t) can be found by convolving the input signal with
h(t):
y(t) = h(t) * x(t)
- h(t) can also be used to find the inverse Laplace transform for a function not in the table of transform pairs
linear time-invariant (LTI) system
a system that is both linear and time invariant
- If an LTI system input is a unit impulse (zero duration, amplitude of 1), then the output is the time-domain equivalent of the system’s Laplace transfer function
system output
the convolution of the input and the time-domain equivalent of the system’s Laplace transfer function is the output
x(t) –> F(s) –> x(t) * f(t)
discrete-time systems
- signals are only defined at discrete sample points
- Discrete points are often given the symbol k rather than t for discrete time
Difference equations
- can be useful in modeling: computer variables in a loop sequential circuits economic situations recursive processes systems with time delays
solving difference equations with z-transforms
Difference equations can be solved by a method similar to that for Laplace transforms
- expand terms
- substitute in terms (y[0], y [1], y[-1])
- manipulate into a form that has an inverse transform
modulation
- process that an information signal is put through to increase its frequency
- combining information signal with a carrier frequency so that modulated signal is at a frequency compatible with the channel for transmission
demodulation
process for reconstructing original information from received modulated signal
modulation process
a) information signal is at baseband frequency
b) carrier signal is at RF frequency of transmission
c) Baseband and carrier are multiplied together in a process called mixing, and the resultant signal is transmitted through the channel
- the source signal is usually converted into a baseband waveform for transmission
- only simple analog systems that directly modulate the carrier do not use a baseband
- the modulator translates the baseband up to an RF frequency for transmission
