Bandpass channels possess a non-zero lower cutoff frequency, and
therefore cannot transmit a baseband signal. For example, the channel
established between two voice-grade telephones begins at 300 Hz and ends at 3,000 Hz.
A digital signal (baseband type) must be shifted in frequency so that its significant
frequency components all exist within the 300 to 3,000 Hz range. Frequency shifting
may be accomplished by impressing the baseband signal onto a sinusoidal
carrier wave.
A sinusoidal carrier wave
c(t)=
A
c
cos(2π
f
c
t+
ϕ
c
)
c(t)=
A
c
cos(2π
f
c
t+
ϕ
c
)
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaaiikaiaadshacaGGPaGaeyypa0JaamyqamaaBaaaleaacaWGJbaabeaakiGacogacaGGVbGaai4CaiaacIcacaaIYaGaeqiWdaNaamOzamaaBaaaleaacaWGJbaabeaakiaadshacqGHRaWkcqaHvpGzdaWgaaWcbaGaam4yaaqabaGccaGGPaaaaa@48DA@
possesses three parameters that can be switched (or keyed) by a binary message signal:
amplitude, frequency, and phase; the resulting
digital continuous wave modulation schemes are called ASK
(amplitude shift keying), FSK (frequency shift keying), and PSK (phase shift keying),
respectively.
The Figure 1 screencast video introduces
the mathematical notation used in this module to discuss ASK modulation, and includes
a visualization of the ASK waveform.
Figure 2 illustrates the block diagram of a
binary ASK transmitter.
The transmitter's signal point mapper selects a value for each bit of
the binary message (bitstream), and the transmit filter generates
an analog signal waveform to be transmitted through the channel. The transmit
filter is also known as the pulse shaping filter.
Binary ASK maps a binary 1 to
E
b
E
b
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and a binary 0 to zero;
E
b
E
b
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denotes the energy per bit. The transmit filter scales a standard pulse shape
by these values to produce the baseband signal, which in turn is shifted in frequency
to match the channel's center frequency by multiplying by a sinusoidal carrier waveform to produce the
transmitted signal.
The Figure 3 screencast video discusses the spectrum of
the transmitted signal, especially the impact of a rectangular pulse shape on the
required bandwidth of the ASK signal.
As discussed in the previous video, the ASK signal created with rectangular pulses is
spectrally inefficient. From an intuitive
point of view, signals with sharp corners always possess a wideband spectrum. Rounding the
corners should therefore produce a transmitted signal that does not require as much bandwidth.
The raised cosine pulse is a standard pulse shape widely used in communication systems that offers much better spectral
efficiency; see the video in pam_RaisedCosinePulse.vi for more background on this important
pulse shape, including an explanation of its excess bandwidth pulse shape parameter.
The Figure 4 screencast video discusses the
spectrum of the transmitted ASK signal with raised cosine pulse shaping.
Consider once again the transmitter block diagram of
Figure 2. In a fully digital implementation, the
pulse shaping filter output must be a sampled-value waveform. Rectangular pulse shapes are easy
to implement: a given binary symbol simply maps to an array of constant values. Nonrectangular
pulses take a bit more effort, however, especially when the pulse shape must extend over more
than one bit interval.
The Figure 5 screencast video describes a
pulse shaping filter implementation that can be used with any
pulse shape. The basic idea involves driving an FIR filter with an impulse train.
"Examines Binary Amplitude Shift Keying (ASK) modulation"