Modulation is the process where by some property of a carrier signal is varied in accordance with the message signal.  It is used to transmit radio waves so that they will not interfere with other waves being simultaneously transmitted. 

Amplitude Modulation

Amplitude Modulation (AM) involves using the message signal to vary the amplitude of the carrier signal.  One of the advantages of using AM modulation over FM and PM is the AM signal is able to occupy a smaller bandwidth than the other signals.  The following equation is use for amplitude modulation:

where Ac is the amplitude of the modulated signal,  f_c is the frequency of the carrier wave signal, m(t) is the message signal, and k_a is the modulation index or the amplitude sensitivity of the modulator. 

The following Matlab function can be use for AM:   amod.m

Frequency Modulation

Frequency modulation is a type of angle modulation performed by integrating the message signal and placing it in the angle modulation equation as the phase angle of the cosine function.  To modulate in FM the following equation must be use:

where Ac is the amplitude of the modulated signal, f_c is the frequency of the carrier wave signal, m(t) is the message signal, and k_f  is known as the modulation index of the signal.  A larger value of k_f will yield a larger bandwidth, but greater power and efficiency as well

The following Matlab function can be use for FM:   fmod.m

Modulating a signal is only useful if it can be successfully received and demodulated.  Demodulating a signal essentially removes the carrier wave leaving only the message, theoretically without noise or interference.  There are different types of demodulation, much like there are different types of modulation.  The two major forms of demodulation are non-coherent and coherent.

Non-Coherent Demodulation

Non-coherent demodulation is necessary when the exact carrier frequency and/or phase are not known.  This is even necessary when a carrier frequency near the actual one is known.  If the demodulating frequency is slightly different than the modulating frequency the resulting message will be distorted.  Some non-coherent systems will use an approximate carrier frequency to filter out some interference, but it is not used in the demodulation algorithm.  Non-coherent systems are also generally easier and cheaper to implement.

Envelope Detector

An envelope detector can be used to track the peaks of the signal waveform.  When a signal is demodulated using an envelope detector, there is usually a DC component of the output.  When the DC output is removed the resulting signal should match the original.  An envelope detector is mainly used to demodulate an AM signal; however it can be used for FM signal as well.

The following Matlab function can be use for AM demodulation by using the envelope detector: envelopd.m

The envelope detector is also used for non-coherent detection of an FM signal.  However, in order to be useful the FM wave must be put through a differentiator called a frequency discriminator. After the derivative of the signal is taken, the resulting amplitude modulated signal is passed through the envelope detector. 

The following Matlab function can be use for FM demodulation using the frequency discriminator: freqdisc.m

Square-Law Detector

The square law detector has a non-linear input-output characteristic.  The square law detector has a non-linear input-output characteristic.  By looking at the square–law detector circuit in the next figure,

the diode is in series with a resistor and can be expressed by the following equation:

where i is the output current, v is the input voltage, and a and b are arbitrary constants. In the previous equation, i can be interpreted as the demodulated signal and v2 as the modulated signal. To recover the signal using the square-law detector, the input signal is squared, and since it is going to create some high frequencies, a low pass filter its going be needed to fully recover the signal.

The following Matlab function can use for AM demodulation by using square-law detector: sqlawd.m

Coherent Demodulation

Unlike non-coherent demodulation, coherent systems require knowledge of the transmitted carrier frequency and phase at the receiver.  In doing so, it can track carrier frequency and phase changes to prevent distortion in the demodulation process.  Since non-coherent systems depend solely on the message signal for demodulation, if that signal picked up any noise during transmission that same noise would cause greater errors at the receiver.

Phase Locked Loop

The phase-locked loop demodulator consists of three basic components.  The first component to operate is the voltage controlled oscillator (VCO) as it outputs a signal with the natural frequency, otherwise known as the carrier frequency.  When this signal reaches the phase detector (PD), along with the input modulated signal that is to be demodulated, the phase detector uses techniques such as multiplication to compare the two signals and output an error signal.  A typical PLL also includes a loop filter, which is basically a low-pass filter in most systems, which filters the error signal from the phase detector.  This final signal is used as input for the VCO which will output another signal tracking the input’s phase and frequency. 

The following Matlab function can be use for PLL: pll.m