EE451L Fall 2009 ______________________________________________________________________________ Amplitude Modulation and Demodulation Introduction A very common method of transmitting information is through Amplitude Modulation (AM) of a message. The transmission of a low-frequency signal over a channel requires a process to transform the signal to a high-frequency. At the receiver end, the signal is demodulated and filtered to extract the low-frequency signal. There are four major types of modulation of signals: amplitude modulation, frequency modulation, phase modulation, and pulse amplitude modulation. In amplitude modulation a transmitted signal includes the carrier signal. An AM signal has the following form )cos()](1[)( twtmkAtscac+= Where Ac is the amplitude of the carrier, ka is the amplitude sensitivity of the modulator, m(t) is the message, and cos(wct) is the carrier. In standard AM modulation, 1+kam(t) ≥ 0 for all t, so the message can be recovered from the envelope to within a scale factor and constant offset. Two methods can be used for envelope detection and are particularly suited for DSP implementation: the square-law and Hilbert transform detection. The square-law demodulation method consists of squaring the signal, passing it though a lowpass filter, obtaining the square root and finally, scaling and removing an offset. The first step can be expressed as )2cos()](1[5.0)](1[5.0)(cos)](1[)(22222222twtmkAtmkAtwtmkAtscacaccac+++=+= The right-hand side of the equation above consists of a lowpass signal whose cutoff frequency has been modified to 2ωs by the squaring operation, and a second term that has a spectrum centered at ± 2ωc. For positive frequencies, the spectrum of the signal has a range of 2ωc ± 2ωs. The spectra of these two terms must not overlap ωc > 2ωs The lowpass filter has a cutoff frequency of 2ωs and its output is 22)](1[5.0 tmkAac+ . Square-root of this signal results in an output signal that is proportional to m(t) with a DC offset, which can be removed by a highpass filter. Assuming that m(t) does not have spectral components below 50Hz, the following highpass filter can be used to remove the DC offset 111121)(−−−−+=czzczGEE451L Fall 2009 ______________________________________________________________________________ Where c is a constant slightly less than 1 so that m(t) does not get distorted. For this project you will need to create an AM modulator. Use fs =48 kHz. For your message, have the program generate a sinusoidal signal. You should be able to vary the message frequency dynamically as your code is running. You may use fdatool from MATLAB to design a filter with the following specifications: Rp = 0.1 dB and Rs = 50 dB, and express it as a cascade of second-order systems. Connect a function generator to the board and vary the frequency and verify that the program can generate an AM signal. You will need another DSP board to generate the