Delta Modulation/Demodulation

  1. Down load the Delta modulation files (tar or zip)
  2. Extract the files (Example: tar xvf dm.tar or unzip
  3. For sample usage, run dm_demo file at the MATLAB prompt

Click here to down load the Delta Modulation files (dm.tar).
Click here to down load the Delta Modulation files (

Delta modulation (DM) may be viewed as a simplified form of DPCM in which a two level (1-bit) quantizer is used in conjunction with a fixed first-order predictor. The block diagram of a DM encoder-decoder is shown below.


The "dm_demo" shows the use of Delta Modulation to approximate a input sine wave signal and a speech signal that were sampled at 2 KHz and 44 KHz, respectively. The source code file of the MATLAB code and the out put can be viewed using MATLAB. Notice that the approximated value follows the input value much closer when the sampling rate is higher. You may test this by changing sampling frequency, fs, value for sine wave in "dm_demo" file.

To view these you need to download the zip or tar  files and sound file into a directory.  if you wish you may modify the dm_demo file any time to see the effect of sampling rate and stepsize, then run demo file on MATLAB. To run the demo file, type "dm_demo" at the MATLAB prompt. (Remember to change directory into the same directory that the files were placed in.) Since DM (Delta Modulator) approximate a waveform Sa(t) by a linear staircase function, the waveform Sa(t) must change slowly relative to the sampling rate. This requirement implies that waveform Sa(t) must be oversampled, i.e., at least five times the Nyquist rate.

"Oversampling" means that the signal is sampled faster than is necessary. In the case of Delta Modulation this means that the sampling rate will be much higher than the minimum rate of twice the bandwidth. Delta Modulation requires "oversampling" in order to obtain an accurate prediction of the next input. Since each encoded sample contains a relatively small amount of information Delta Modulation systems require higher sampling rates than PCM systems. At any given sampling rate, two types of distortion, as shown below limit the performance of the DM encoder.

  1. Slope overload distortion: This type of distortion is due to the use of a step size delta that is too small to follow portions of the waveform that have a steep slope. It can be reduced by increasing the step size.

  2. Granular noise: This results from using a step size that is too large too large in parts of the waveform having a small slope. Granular noise can be reduced by decreasing the step size.

Even for an optimized step size, the performance of the DM encoder may still be less staisfactory. An alternative solution is to employ a variable step size that adapts itself to the short-term characteristics of the source signal. That is the step size is increased when the waveform has a step slope and decreased when the waveform has a relatively small slope. This strategy is clalled adaptive DM (ADM).

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