Chapter 6 - Amplitude Modulation (AM) Theory and Simulation

Mixes ("heterodynes") the information signal with a carrier signal, called Double Sideband (AM-DSB). The information signal is "shifted up" from baseband to a carrier frequency.

Two variations:

AM-DSB-SC (Suppressed Carrier AM)

AM-DSB-TC (Transmitted Carrier AM)

Information signal si(t) plus DC offset Ao is multiplied with carrier sc(t), result is sam-dsb-tc(t) = [Ao + si(t)] * sc(t)

= Ao*Ac*cos(wc)*t + (AiAc/2)(cos(wc - wi)t + cos(wc + wi)t)

Alternative representation uses AM modulation index 'm':

m can be expressed as a percentage. The max value of m which preserves the information envolope is 1 (100%)

AM-SSB (Single Sideband AM)

Double Sideband AM uses twice the bandwidth of the information signal; Single Sideband AM uses the same amount of bandwidth

Modulated signal is calculated via:

The results are:

In the diagram, only one of the outputs is used; it just shows both options for either upper sideband (susb) or lower sideband (slsb)

The difference between the upper and lower sideband modulations is that the modulated signal for lower sideband is to the left (lower) of the carrier frequency while the modulated upper sideband is to the right (higher) of the carrier frequency:

AM-VSB (Vestigial Sideband AM)

Uses a bandpass filter (BPF) on Transmitted Carrier (TC) AM to further reduce bandwidth. The reduced width sideband is called a Vestigial Sideband

The modulated signal is BPF([Ao + si(t)]sc(t))

Theoretical AM Demodulation

To demodulate an AM signal, it must be multiplied with the EXACT frequency and phase which was used as the carrier signal; however it is unlikely that these exactly match on the receiving end

RTL-SDR demodulation

The signal the RTL sdr uses to get its IQ samples from, when receiving AM-DSB-TC signals is:

However, this assumes the oscillator frequency exactly matches the carrier frequency. This there is an additional frequency offset used in actual demodulation

Non-coherent AM demodulation (for dsb-tc AM)/Envolope Filter

Simplest non-coherent demodulator is the "envelope detector": a lowpass filter which smooths gaps between the pearks of the carrier wave

Digital, software implementation is as follows:

This way however will struggle if the carrier frequency is low

Optimized version is as follows:

Complex Envolope Filter

No low pass filter required; converts both the in-phase and quadrature components of the complex input signal to magnitude. This is the equivalent of the radius between the two signals between the I and Q plane:

This is the most optimized version; recommends using