Digital signal (signal processing)

In other words, it is a sampled signal consisting of samples that take on values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers).

Most commonly, these discrete values are represented as fixed-point words (either proportional to the waveform values or companded) or floating-point words.

[1][2][3][4][5] The process of analog-to-digital conversion produces a digital signal.

[6] The conversion process can be thought of as occurring in two steps: An analog signal can be reconstructed after conversion to digital (down to the precision afforded by the quantization used), provided that the signal has negligible power in frequencies above the Nyquist limit and does not saturate the quantizer.

A floating point representation is used in many DSP applications.

The red digital signal is the sampled and quantized representation of the gray analog signal. A digital signal consists of a sequence of samples, which in this case are integers: 4, 5, 4, 3, 4, 6...
Discrete cosine waveform with a frequency of 50 Hz and a sampling rate of 1000 samples/sec, efficiently satisfying the sampling theorem for the reconstruction of the original cosine function from samples. (The effects of quantization are too subtle to be seen in this graph.)