Presentation 02
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Pulse modulation is a technique used to transmit analog information
by converting it into a series of discrete pulses. In pulse modulation, the
continuous analog signal is sampled, and these samples are then used
to modify a series of pulses in some manner.
There are several types of pulse modulation, including:
1. Pulse Width Modulation (PWM): The width of each pulse is varied in proportion to the
amplitude of the analog signal at the time of sampling. Common applications include
power delivery, voltage regulation and motor controls
2. Pulse Position Modulation (PPM): The position of each pulse within a time slot is
varied according to the amplitude of the analog signal. Commonly used for RF
communications as it tends to require simple and thus light weight electronics
3. Pulse Amplitude Modulation (PAM): The amplitude of each pulse is varied based on the
amplitude of the analog signal. It is mostly used as an intermediate form of modulation
and is seldomly used by itself.
4. Pulse Code Modulation (PCM): The analog signal is sampled, and each sample is
quantized and then encoded into a binary code for transmission. PCM is the most
common form of pulse modulation used in digital communication systems.
Pulse Code Modulation (PCM) was invented by Alec H. Reeves in 1937 while
working for AT&T in Paris. Although recognized for its merits early on, PCM only
became widely prevalent in the mid-1960s with the development of solid-state
electronics
Pulse Code Modulation (PCM) was invented by Alec H. Reeves in 1937 while
working for AT&T in Paris. The potential of PCM was recognized early on, but the
technology of the time posed significant challenges. The primary issue was the
complexity of the required circuitry, which cannot be implemented with with the
vacuum tube technology available at that time. The invention of the transistor and
the development of solid-state electronics in the 1960s provided the necessary
technological as they were smaller, more reliable, and consumed less power,
making it feasible to implement PCM in practical applications.
A Pulse Code Modulation (PCM) system consists of several basic elements that
work together to convert an analog signal into a digital format, transmit it, and
then reconvert it back into analog form at the receiver. These elements are
crucial for ensuring the accurate and efficient transmission of data.
1. Low Pass Filter: used to limit the frequency range of the input
analog signal to prevent aliasing. It removes any high-frequency
components that are higher than the Nyquist frequency, ensuring
that the signal is band-limited before sampling.
2. Sampler: periodically samples the amplitude of the filtered analog
signal at regular intervals. According to the Nyquist theorem, the
sampling rate must be at least twice the highest frequency present
in the analog signal to accurately capture the signal's information.
3. Quantizer: converts each sampled amplitude into one of a finite
number of levels. It essentially rounds off the sampled values to the
nearest level within a predefined range, introducing a quantization
error or noise.
4. Encoder: converts the quantized samples into a binary code. Each
quantized level is assigned a unique binary number, and these
binary codes are then transmitted as a series of pulses
5. Regenerative Repeater(Optional): used to regenerate and amplify
the digital signal as it travels over the transmission medium. They
help to maintain the integrity of the signal by reducing the effects of
noise and signal degradation.
6. Decoder: converts the binary PCM code back into its corresponding
quantized amplitude levels. This is the reverse of the encoding
process
7. Reconstruction Filter: typically a low-pass filter, smoothens the
output of the decoder to reconstruct the analog signal from the
quantized samples. It removes the high-frequency components
introduced during the sampling and quantization processes.
8. Output Transducer: converts the reconstructed electrical signal
back into its original physical form, such as sound through a speaker
Sampling
Sampling is defined as the process
of measuring the instantaneous
values of continuous-time signal in
a discrete form.
Sampling rate(fs) is the rate at
which samples are taken from the
original analog signal.
Sampling period(Ts) is the gap in
between samples.
1
𝑓𝑠 =
𝑇𝑠
Sampling
Aliasing is an error caused by under sampling. Because of this, the
signal is misidentified and later on misrepresented. To prevent this
from happening, low pass anti-aliasing filters can be employed
before the sampler, ensuring that high frequency components
cannot make it to the sampling stage
Sampling
Nyquist Theorem says that the minimum sampling rate must be at
least twice the highest frequency of the analog input to avoid aliasing.
If the sampling rate is below this threshold, foldover distortion occurs,
causing a loss of information. The Nyquist rate can be defined as:
𝑓𝑛 ≥ 2𝑓𝑎
where fa is the maximum analog input frequency.
Sampling
Essentially, there are two basic techniques used to perform the sampling
function:
1. Natural Sampling: This technique involves sampling the analog signal
where the tops of the sample pulses retain their natural shape during the
sampling interval. However, this method is challenging for analog-to-digital
conversion (ADC) because the signal voltage can change during the
sampling period, making it difficult for the ADC to stabilize on a particular
PCM code. The frequency spectrum of the output differs from an ideal
sample, often requiring frequency equalizers before recovery.
Sampling
2. Flat-Top Sampling: This method uses a sample-and-hold circuit to produce
constant-amplitude pulses. The sampled voltage is held constant until the
next sample is taken, reducing aperture distortion and allowing the ADC to
operate more efficiently. This is the most common method used in PCM
systems for voice signal sampling.
Quantization
Quantization: is the process of converting the sampled analog signal into a
digital signal by assigning each sample to the nearest value from a finite set of
levels. This step is necessary after sampling to reduce the continuous
amplitude of the signal to discrete levels, enabling binary encoding.
Quantization
Quantization Error: This error arises because the original signal amplitude
rarely matches one of the discrete levels exactly. The maximum magnitude of
the quantization error is typically equal to half the quantization interval. This
error manifests as quantization noise, which adds a small distortion to the
signal. This error is inevitable, but can be minimized by using more bits
Encoding
Encoding : involves converting the quantized values into a binary format. Each
quantized level is assigned a unique binary code, which represents the
amplitude of the sampled signal at that particular instant. The binary
representation of the analog signal can then be transmitted digitally.
