# Analog and Digital Conversion/Delta Modulation

## Contents

## Delta Modulation[edit]

The sample values of analog waveforms of real world processes are very often predictable -- i.e. the average change from sample to sample is very small. Hence we can make "educated guess" of what the next sample value depending on the current sample value. Though there is error, it is much less than peak to peak signal range. This concept is used in **Predictive coded modulation**, where instead of sending the signal, it transmits just the prediction errors. Delta Modulation employs Predictive coded modulation to simplify hardware

**Delta Modulation** is strange in the fact that it attempts to represent an analog signal with a resolution of 1 bit. This is accomplished by successive steps, either up or down, by a preset step size. In delta modulation, we have the stepsize (Δ) that is defined for each sampler, and we have the following rules for output:

- If the input signal is higher than the current reference signal, increase the reference by Δ, and output a 1.
- If the input signal is lower than the current reference signal, decrease the reference by Δ, and output a 0.

Some benefits of delta modulation are as follows:

- 1 bit of resolution, and therefore requires very little bandwidth and very little hardware.
- No preset upper or lower bounds, so Delta modulation can (theoretically) be used to modulate unbounded signals.

These benefits are countered by the problems of **Slope Overload**, and **Granular Noise**, which play an important role when designing a Delta Modulated system.

## Slope Overload[edit]

If the input signal is rising or falling with a slope larger than Δ/T, where T is the sampling time, we say that the sampler is suffering from **Slope Overload**. In essence, this means that in a Delta Modulation scheme, we can never have slopes larger than a certain upper limit, and functions that rise or fall at a faster rate, are going to be severely distorted. If the slope of m(n Ts)is greater then the slope of m(n Ts- Ts), then Slope Overload distortion occurs.

## Granular Noise[edit]

A problem with delta modulation is that the output signal must always either increase by a step, or decrease by a step, and cannot stay at a single value. This means that if the input signal is level, the output signal could potentially be oscillatory. That is, the output signal would appear to be a wave, because it would go up and down regularly. This phenomena is called **Granular Noise**.

When used in ADCs (Analog to Digital Converters), this problem can be solved by internally adding additional bit(s) of resolution that correspond to the value of Δ. This way, the LSBs (Least significant bits) that were added can be ignored in the final conversion result.

## Delta-Sigma Modulation[edit]

A delta-sigma ADC -- also called a sigma-delta ADC -- use the delta modulation technique internally.