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If the signal is transmitted at a carrier frequency , then the so that an antenna whose length is cm which is much more manageable for the pigeon.
5/ Narrow-band signals
The modulated transduced pigeon sound has a spectrum that is centered about the carrier frequency and has a bandwidth of where is the maximum frequency of the pigeon sound.
For the pigeon sound we have = 3 kHz and = 600 MHz. Thus, the bandwidth is only of the carrier frequency — an example of a narrowband signal.
An arbitrary narrowband signal can be expressed as
where and are lowpass time functions. We can expand x(t) as follows
Where
An arbitrary narrowband signal can be written as
Thus, a general narrowband signal contains both amplitude and phase/frequency modulation. In amplitude modulation (AM) is constant; in phase/frequency modulation (PM or FM) a(t) is constant.
II. AMPLITUDE MODULATION
1/ AM, suppressed carrier
Perhaps the simplest amplitude modulation scheme is the suppressed carrier scheme in which
Therefore, the Fourier transform is
The Fourier transform of the modulated signal x(t) can be obtained graphically.
The Fourier transform is repeated at .
2/ Demodulation (detection) of AM, suppressed carrier
The original signal can be recovered by modulating the modulated signal and passing the result through a lowpass filter, a process called demodulation or detection.
3/ AM, suppressed carrier radio
A radio communication system that consists of a transmitter and receiver and which uses suppressed carrier AM is shown below.
Therefore,
Hence,
The spectrum of y(t) involves the spectrum of which can be found by the trigonometric identity or as shown below.
can be written as
The Fourier transform of is shown below.
Thus, using Fourier transform properties it is easy to derive trigonometric identities.
Two-minute miniquiz problem
Problem 23-1 — AM, suppressed carrier radio
A slight alternative to the AM suppressed carrier radio system is shown below.
Using an appropriate low pass filter, H(f), to detect , determine the spectrum .
Solution
We need to convolve the spectrum of the modulated function X(f) with the Fourier transform of .
Thus, the output is zero.
The following reviews the results for suppressed carrier radio.
Suppressed carrier AM requires that the transmitter and receiver be perfectly synchronized. A small difference in frequency of transmitter and receiver oscillators results in a drift in the phase difference between the oscillators which causes variations in the amplitude of the detected signal, called signal strength fading.
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