### Analog to Digital – A/D conversion steps

The A/D conversion (coding) involves:

**Sampling:**measuring the amplitude values (or function values) at a finite number of positions.**Quantization:**representing the amplitude values by a finite number of natural numbers.

We could have different sampling steps along the sampling axis, but in most cases we assume Regular (equidistant) sampling. Even under regular sampling, one must decide –

Where do we take the samples along the analog signal so that we can properly reconstruct the original function. Along the vertical axis we also have continuous values that we can only store using a finite number of natural numbers.

**Typical image options:**

8-12 bits per pixel for gray scale images.

8 bits per color channel (R,G,B) per pixel for color images.

1 bit per pixel for black/white images.

special encoding per application.

Unlike sampling, quantization intervals are often not equidistant. In the case of non-uniform quantization, the

behavior of the quantizer is decided by the characteristic function.

**A/D analysis tools: **

In order to fulfill the necessary performance guarantees (accurate reconstruction) we need to use the appropriate tools.

**Sampling Tool: Fourier Analysis – **Fourier Analysis allows us to study signals as a collection of periodic

signals. This periodicity then guides the sampling rate.

**Quantization Tool: Probability Theory – **Study previous behavior of the signal. High probability values use

dense quantization. Lower probability values use sparse quantization.