# Analog Pulse Modulations: PAM AND PWM

|Communication systems play an important role in all the information transmission systems. Generally, in all the communication systems, the information in the source is processed through a modulator in order to make it suitable to the communication channel. The inverse process happens at the received side.

**study of the analog pulse modulations**.

**advantages of using digital modulation**instead of analag modulation. Some of them are:

- Noise immunity: analog signals are weaker than pulses facing non-desired amplitudes, frequencies and phase changes.
- Digital pulses are easier to process and send through multiple channels than analog signals.
- Digital systems use signal recovering instead of signal amplifying; therefore they provide a stronger system to face the noise in comparison with the analog case.
- Digital signals are easier to measure and evaluate.
- Digital systems are better equipped to evaluate errors (for instance, error detection and correction) than analog systems.

**the information source can also be analog, as it’s the case of the voice**: in order to transmitted as a digital signal, Pulse Code Modulation (PCM) or other techniques more advanced, such as analog to digital conversion, are used by the codec devices.

**PAM and PWM**.

**our next post: the corresponding Matlab Tutorial.**We will also provide a

**Simulink model**🙂

**PAM (PULSE AMPLITUDE MODULATION)**

_{p}[t] , with a rectangular pulse, h[t]:

**Nyquist condition**will be met if: T=Ts/2. Also, we know that the bigger T is, the smaller bandwidth the modulated signal will have.

**Fourier Transform of a PAM signal**is:

**Fourier Transform of a rectangular pulse**:

**PWM (PULSE WIDTH MODULATION)**

**PWM technique reduces the noise sensitivity**and keeps the same spectrum as a PAM signal for t << T where t and T are the pulse duration and the sequence period respectively.

**DC component**, something that we need to bear in mind when looking at the spectrum.

The next step in the PWM signal generation is to apply a comparator to the last signal and this will results in an output when the voltage is greater than a certain threshold (for instance, 2V) and zero, when is lower. The result is a signal formed by a of variable duration pulses. In the next image, on the left, we have drawn the information signal on top, so you can appreciate the pulse’s width variation according to it: the pulses width increases in the positive cycles of the information signal and vice-versa. On the right side, you can observe the PWM signal.

**repeated in the multiples of the frequency of the triangular signal**.

_{s}[n] represent the signal x[n] once is sampled so x

_{s}[n]=x[n]p[n], p[n] is the sampling function that, in this case, we can consider a periodic sequence of pulses (therefore, p[n] can be described using the Fourier series).

_{s}[n], is formed by the spectrum of x[n] shifted to the multiples of the sampling frequency. If

**x[n] is bandwidth-limited, we can get it back by using the Nyquist theorem**:

*The Nyquist Theorem states that a bandwidth limited signal, x[n], with no frequency components greater than fm Hz, is completely defined by a set of samples taken at a 2xfm Hz rate. Therefore, the time between samples can’t be greater than 1/2 x fm.*

**Matlab and Simulink tutorial where we will see exercises and code for these two modulations**!