4.0 Pulse Modulation Techniques
4.0 Pulse Modulation Techniques
Pulse modulation techniques operate on signals that are discrete in time. The conversion from a continuous signal to a discrete one is achieved through sampling.
4.1 The Role of Sampling (Nyquist Theorem and Aliasing)
Sampling is the process of converting a continuous-time signal into an equivalent discrete-time signal by taking measurements at regular intervals (T_s). The Sampling Theorem, or Nyquist theorem, states that a signal can be perfectly reconstructed if it is sampled at a rate (f_s) greater than or equal to twice its maximum frequency (W).
f_s ≥ 2W
This minimum sampling rate (2W) is known as the Nyquist rate. If a signal is sampled at a rate less than the Nyquist rate, Aliasing occurs, where high-frequency components of the signal impersonate lower-frequency components, leading to irreversible information loss.
4.2 Analog Pulse Modulation
In analog pulse modulation, a characteristic of a pulse train (amplitude, duration, or position) is varied in accordance with the message signal.
| Modulation Type | Varied Parameter | Key Characteristics | Similar To | Noise Interference |
| Pulse Amplitude Modulation (PAM) | Amplitude | Instantaneous transmitter power varies. | Amplitude Modulation | High |
| Pulse Width Modulation (PWM/PDM) | Width / Duration | System complexity is low. | Frequency Modulation | Low |
| Pulse Position Modulation (PPM) | Position | Amplitude and width are constant; power is constant. Requires synchronization. | Phase Modulation | Low |
4.3 Digital Pulse Modulation (PCM)
Pulse Code Modulation (PCM) is the primary technique for converting an analog signal into a digital binary sequence (1s and 0s). This process makes the signal robust and suitable for digital transmission and processing.
Process: Sampling, Quantizing, Encoding
- Sampling: The analog signal is sampled at a rate at or above the Nyquist rate. A Low Pass Filter is used before sampling to prevent aliasing.
- Quantizing: The continuous amplitude of each sample is rounded off to one of a finite set of discrete levels. This process introduces quantization error but is necessary for digitization.
- Encoding: Each quantized level is assigned a unique binary code.
System Components and Signal Reconstruction
- Transmitter (A/D Converter): Consists of a Low Pass Filter, Sampler, Quantizer, and Encoder.
- Receiver (D/A Converter): Consists of a Regenerative Repeater (to reshape and amplify the signal), a Decoder (to convert binary code back to quantized levels), and a Reconstruction Filter (a low pass filter to smooth the output into the original analog signal).