A digital signal is superior to an analog signal.
The tendency today is to change an analog signal to digital data.
In this section we describe two techniques, pulse code modulation and delta modulation

Components of PCM encoder
Three different sampling methods for PCM

Nyquist sampling rate for low-pass and bandpass signals

According to the Nyquist theorem,
the sampling rate must be at least 2 times the highest frequency contained in the signal

Recovery of a sampled sine wave for different sampling rates

Sampling at the Nyquist rate can create a good approximation of the original sine wave.

Oversampling can also create the same approximation, but is redundant and unnecessary.

Sampling below the Nyquist rate does not produce a signal that looks like the original sine wave.

Sampling of a clock with only one hand

The second hand of a clock has a period of 60 s.
According to the Nyquist theorem, we need to sample hand every 30 s


An example of under-sampling is the seemingly backward rotation of the wheels of a forward-moving car in a movie.
A movie is filmed at 24 frames per second.
If a wheel is rotating more than 12 times per second, the under-sampling creates the impression of a backward rotation.

Telephone companies digitize voice by assuming a maximum frequency of 4000 Hz.
The sampling rate therefore is 8000 samples per second


A complex low-pass signal has a bandwidth of 200 kHz.
What is the minimum sampling rate for this signal?

The bandwidth of a low-pass signal is between 0 and f, where f is the maximum frequency in the signal.
Therefore, we can sample this signal at 2 times the highest frequency (200 kHz).
The sampling rate is therefore 400,000 samples per second

Quantization and encoding of a sampled signal

We have a low-pass analog signal of 4 kHz.
If we send the analog signal, we need a channel with a minimum bandwidth of 4 kHz.
If we digitize the signal and send 8 bits per sample, we need a channel with a minimum bandwidth of 8 × 4 kHz = 32 kHz

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