# Pulse Amplitude Modulation

Cuthbert Nyack
This type of modulation is used as the first step in converting an analog signal to a discrete signal or in cases where it may be difficult to change the frequency or phase of the carrier. In this case the carrier is a pulse train rather than a sine wave and the spectrum of the carrier consists of several components around nwc = 2np/T where T is the time between pulses. The spectrum also contains a component at the modulating frequency which may be used to recover the modulating signal. Unipolar PAM also has an average value at w = 0.
The applet below shows some aspects of PAM signals.
Different cases can be seen by varying Fn which is set by scrollbar '0'.

Fn = 0 shows the modulating signal, the carrier and the PAM.
Fn = 1 Shows the Frequency spectrum for unipolar PAM which has an average value at 0 frequency.
Fn = 2 Shows the Frequency spectrum for bipolar PAM which does not have a component at 0 frequency.
Fn = 3 shows the PAM signal reconstructed from the spectrum. The spectrum often quoted for PAM is obtained by multiplying a pulse sequence by a modulating signal. This produces a pulse sequence whose amplitude follows the modulating signal as shown by Fn = 4.
In practice it is more convenient to have a constant amplitude pulse sequence. Fn = 5 shows that the accuracy of the spectral representation increases as the pulse width is reduced.

Fn = 6 shows the signal which results if the PAM is passed through an ideal LP filter whose BW is set by ns and phase at cut off is set by ff.
Fn = 7 and 8 shows the PAM and its spectrum when the modulating signal is a triangular and modified triangular waveform respectively.
Fn = 9 and 10 shows what happens when the PAM is passed through an RC circuit with time constant t1.
Fn = 11, 12 and 13 shows that the output from the RC circuit with time constant t2 is improved if the value of the pulse is sampled and held until the next pulse arrives.
PAM is used as the first step to produce a PCM signal.
Fn = 14 shows the PAM being quantized and the resulting quantization noise. The number of bits is set by Nb and shows that the quantization noise reduces as Nb is increased.
Fn = 15 and 16 show special cases of Fn = 14 with 3 and 6 bit quantization respectively.
PAM allows several signals to be transmitted across a channel using Time Division Multeplexing(TDM). Fn = 17 shows what is meant by TDM. 2 PAM signals shown as red and yellow with modulating signals shown as orange and pink are combined to form the green signal which is then transmitted.