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
single sideband AM (SSB-AM)
- single sideband AM can be generated by filtering out the undesired sideband
- it can be difficult to implement because the filters need sharp corners, especially when the signal has low-frequency content
- imperfectly removed sideband results in distortion
- if there are no low frequencies of interest, filtering can work well (as with voice communication)
- if some portion of the carrier is retained after filtering, the SSB-AM is called vestigial SSB
- the carrier aids in demodulation
phase angle modulation
- varies the angle of the waveform in proportion to the amplitude of the modulating signal
- two types:
- -> frequency modulation (FM)
- -> phase modulation (PM)
frequency modulation (FM)
- the instantaneous frequency deviation of the carrier wave varies in proportion to amplitude of the modulating signal
- kf is the frequency deviation constant in radians per second per unit of m(t)
demodulator
replicates the baseband signal except for distortion and noise introduced by the channel
AM demodulation
- Demodulation of AM can be done with an envelope detector followed by a low-pass filter
- An ideal envelope detector produces a signal proportional to the envelope of the modulated signal
- In practice, envelope detectors are rectifier circuits with long time constants
- Demodulating of AM can also be done with coherent demodulator (called phase-coherent or phase-synchronized demodulation)
- SSB signals can be demodulated with a synchronous demodulator or by carrier reinsertion and envelope detection
FM and PM demodulation
- frequency modulation can be demodulated using an ideal phase detector
- voltage output of ideal phase detector is proportional to phase deviation of the intermediate frequency signal
- practical phase detectors involve sine wave phase comparisons
- in phase modulation, the frequency deviation ratio must be less than equal to pi to avoid ambiguity in the demodulatin
- limitations make PM less popular than FM
phase-locked loop (PLL)
- circuit that performs demodulation of angle modulation (either FM or PM)
- uses feedback tracing (for this reason also called phase-tracking loop)
- is less susceptible to variation in circuit parameters due to feedback
- needs less carrier power for demodulation than previous discriminator methods
- voltage- controlled oscillator (VCO) nominally at intermediate frequency (IF)
- VCO output frequency proportional to input voltage
- band-pass filter characteristics chosen to reduce noise and limit distortion
- also used DSB-AM demodulation
time multiplexing
technique allowing more than one signal to share communication channel at one time
-can be analog or digital
pulse amplitude modulation (PAM)
- a method for sampling and holding an analog signal, then sending the samples as pulses
- values may be discrete or continuous
- usually refers to signal in which amplitude is proportional to the input samples
time multiplexing techniques
- pulse amplitude modulation (PAM)
=> method for sampling and holding analog signal, then sending samples as pulses
-pulse-width modulation (PWM)
=> uses constant-amplitude pulses, width proportional to the input samples
-pulse-position modulation (PPM)
=> constant amplitude and width of pulses, but time between pulse positions proportionate to input samples
pulse-code modulation (PCM)
means of sending digitally coded information in discrete values
-binary on-off keying (BOOK)
carrier or modulation signal can be turned on or off to represent 1 or 0
- binary phase shift keying (BPSK)
phase shifts of discrete values represent 1 or 0
-binary frequency shift keying (BFSK)
frequency shifts of discrete values to represent 1 or 0
Advantages of PCM include:
- digital words can have many sources, and are loaded in a shift register for serial transmission
- handled very easily by computer
- long-distance transmission with retransmission can be done with no loss in signal quality
- integrated circuits can be used for high reliability and stability
- data compression can be used for faster transmission
- the modulating signal is sample d at fixed, intervals, resulting in an analog quantized signal
- Quantized signal is digitized by an analog-to-digital converter. Digital bits are sent over communication channel
- If n-bit binary words are used to represent modulating signal m(t), the number of possible quantization levels that can be represented is a=2^N
- of m(t) has maximum frequency of fm, sampling frequency is 2fm. if number of bits per sample is n, PCM system will send 2nfm pulses per second
sampling
continuous-time signals are sampled to a discrete-time system
the analog signal is sampled at regular time intervals, delta t
Shannon’s sampling theorem
a time-continuous signal can be completely reconstructed from a sequence of equally spaced values, if the sampling rate is at least twice the highest frequency component, the frequency of interest, fN (sometimes given as f1)
Nyquist rate, 2fN
The minimum acceptable sampling rate if the signal is to be reproduced from its samples
- Sampling at the Nyquist rate is enough for most practical applications
- When sampling is less than Nyquist rate, data will contain false spectral content (called aliasing) for any frequencies greater than half the sampling frequency
filter
a component that allows only parts of the signal to get through h
- An example is the parallel band-pass filter at night
- The voltage across the parallel component, v2, is a function of the frequency
- the transfer function is derived from Kirchoff’s laws using the Laplace impedance
filter
- bandwidth is difference between upper and lower half-power frequencies
- at resonance, magnitude of transfer function in frequency domain is purely resistive, meaning input and output voltage are in phase and output power is maximum
- bandwidth of filter depends on resistance and capacitance for circuit
