Digital-to-Analog Converter

A Digital to Analog Converter (DAC) converts digital data to an impulse train, then pass the result through a low pass filter with a cutoff frequency equal to the Nyquist frequency (one half of the sampling rate) to obtain a reconstructed analog signal .

In practice, a zero-order hold technique is used. It consists in keeping the last value until a new sample value occurs. We obtain a signal with straircases. This signal is equivalent to the convolution of an impulse train with a rectangular window function. In the frequency domain, it is equivalent to the multiplication of the spectrum of the impulse train by the spectrum of the rectangular window, e.g. a sinc function (sinc(x) or sin(pi*x)/(pi*x)).

The filter used to transform the zero-order signal to its analog version processes two main tasks:

1. remove all frequencies above the nyquist frequency 
2. amplify the signal by 1/sinc(x) or 1/sinc(f/fs) where fs is the sampling frequency. 

The last function (2.) can be realized in differents ways: ignore and assume the consequences, include it in the filter design, use a multirate technique or software correction before DAC.

Note: Analog and digital signals are both limited by noise and by the highest frequency (or bandwith).
A digital signal sampled at 20kHz carries exactly the same information as the analog signal with frequencies between 0 and 10kHz.

@uthor: Joan MOUBA.