COMPARISON OF VARIOUS PULSE ANALOG MODULATION METHODS (U.P. Tech, Semester Examination, 2003-04)
In this section, let us compare PAM, PWM and PPM in the form of a Table 3.2.
Table 3.2. Comparison of PAM, PPM and PDM
| S. No. |
Pulse Amplitude Modulation (PAM) | Pulse Width/Duration Modulation (PWM) or (PDM) | Pulse Position Modulation (PPM) |
| 1 | DIAGRAM | DIAGRAM | DIAGRAM |
| 2 | Amplitude of the pulse is proportional to amplitude of modulating signal. | Width of the pulse is proportional to amplitude of modulating signal. | The relative position of the pulse is proprotional to the amplitude of modulating signal. |
| 3 | The bandwidth of the transmission channel depends on width of the pulse. | Bandwidth of transmission channel depends on rise time of the pulse. | Bandwidth of transmission channel depends on rising time of the pulse. |
| 4 | The instantaneous power of the transmitter varies. | The instantaneous power of the transmitter varies. | The instantaneous power of the transmitter remains constant. |
| 5 | Noise interference is high System is complex. | Noise, interference is minimum. | Noise, interference is minimum. |
| 6 | Similar to amplitude modulation. | Simple to implement similar to frequency modulation. | Simple to implement similar to phase modulation. |
SUMMARY
■ There are two types of signals, continuous time signal and discrete-time signals.
■ Due to some recent advance development in digital technology over the past few decades, the inexpensive, light weight, programmable and easily reproducible discrete-time systems are available. Therefore, the processing of discrete-time signals is more flexible and is also preferable to processing of continuous-time signals.
■ The sampling theorem is extremely important and useful in signal processing.
■ With the help of sampling theorem, a continuous-time signal may be completely represented and recovered from the knowledge of samples taken uniformly.
■ The concept of sampling provides a widely used method for using discrete-time system technology to implement continuous-time systems and process the continuous-time signals.
■ Sampling of the signals is the fundamental operation in signal-processing. A continuous time signal is first converted to discrete-time signal by sampling process.
■ The sufficient number of samples of the signal must be taken so that the original signal is represented in its samples completely. Also, it should be possible to recover or reconstruct the original signal completely from its samples. The number of samples to be taken depends on maximum signal frequency present in the signal.
■ A continuous-time signal may be completely represented in its samples and recovered back if the sampling frequency is fs > 2 fm. Here, fs is the sampling frequency and fm, is the maximum frequency present in the ‘signal.
■ When the sampling rate becomes exactly equal to 2fm, samples per second, then it is called Nyquist rate. Nyquist rate is also called the minimum sampling rate. It is given by
fs = 2fm
■ Maximum sampling interval is called Nyquist interval. It is given by
Nyquist Interval Ts =
■ The low pass filter is used to recover original signal from its samples. This is also known as interpolation filter.
■ A low-pass filter is that type of filter which passes only low-frequencies upto a specified cut-off frequency and rejects all other frequenices above cut-off frequency.
■ The process of reconstructing a continuous-time signal x(t) from its samples is called as interpolation.
■ Aliasing is the phenomenon in which a high frequency component in the frequency-spectrum of the signal takes identity of a lower-frequency component in the spectrum of the sampled signal.
■ Because of the overlap due to alisising phenomenon, it is not possible to recover original signal x(t) from sampled signal g(t) by filtering since the spectral components in the overlap regions add and hence the signal is distorted.
■ Since any information signal contains a large number of frequencies, so, to decide it sampling frequency is always a problem. Therefore, a signal is first passed through a low-pass filter. This low-pass filter blocks all the frequencies which are above fmHZ. This process is known as band limiting of the original signal x(t). This low-pass filter is called prelias filter because it is used to prevent, abasing effect.
■ To avoid abasing, we must have:
(i) Preaias filter must be used to limit hand of frequencies of the signal to fmHz.
(ii) Sampling frequency ‘fs‘ must be selected such that
fs > 2fm
■ The bandpass signal x(t) whose maximum bandwidth is 2fm can be completely represented into and recovered from its samples if it is sampled at the minimum rate of twice the bandwidth. Here, fm is the maximum frequency component present in the signal.
■ Basically, there are three types of sampling techniques as under:
(i) Instantaneous sampling
(ii) Natural sampling
(iii) Flat top sampling.
■ Natural sampling is a practical method and will be discussed in this section.
■ Spectrum of Naturally Sampled signal:
■ Flot top sampling like natural sampling is also a practically possible sampling method. But natural sampling is little complex whereas it is quite easy to get flat top samples.
■ Spectrum of flat top sampled signal:
■ In analog modulation systems, some parameter of a sinusoidal carrier is varied according to the instantaneous value of the modulating signal. In pulse modulation methods, the carrier is no longer a continuous signal but consists of a pulse train. Some parameter of which is varied according to the instantaneous value of the modulating signal.
■ There are two types of pulse modulation systems as under:
(i) Pulse Amplitude Modulation (PAM)
(ii) Pulse Time Modulatin (PTM)
■ In pulse amplitude modulation (PAM), the amplitude of the pulses of the carrier pulse train is varied in accordance with the modulating signal whereas in Pulse time modulation (PTM), the timing of the pulses of the carrier pulse train is varied.
■ They are two types of PTM as under:
(i) Pulse width modulation (PWM)
(ii) Pulse position modulation (PPM).
■ In Pulse width modulation, the width of the pulses of the carrier pulse train is varied in accordance with the modulating signal whereas in Pulse position modulation (PPM), the position of pulses of the carrier pulse train is varied.
■ It may be noted that all the above pulse modulation methods (i.e., PAM, PWM and PPM) are called analog Pulse modulation methods because the modulating signal is analog in nature in PAM, PWM and PPM.
■ Pulse amplitude modulation may be defined as that type of modulation in which the amplitudes of regularly spaced rectangular pulses vary according to instantaneous value of the modulating or message signal. In fact, the pulses in a PAM signal may be of flat top type or natural type or ideal type. Actually all the sampling methods which have been discussed in last sections are basically pulse amplitude modulation methods.
■ BW of PAM signal is given by
But
Hence
Again, since
Therefore
■ If the PAM signals are to be transmitted directly i.e., over a pair of wires then no further signal processing is necessary. However, if they are to be transmitted through the space using an antenna, they must first be amplitude or frequency or phase modulated by a high frequency carrier and only then they can be transmitted.
■ The bandwidth required for the transmission of a PAM signal is very very large in comparison to the maximum frequency present in the modulating signal.
■ Since the amplitude of the PAM pulses varies in accordance with the modulating signal therefore the interference of noise is maximum in a PAM signal. This noise cannot be removed easily.
■ Since the amplitude of the PAM signal varies, therefore, this also varies the peak power required by the transmitter with modulating signal.