# Delta Modulation With It’s Block Diagram

When signals are transmitted over long distances, they get affected by noise and interference. There are several methods invented for effective transmission of signals over long distances without any error. The conversion of analog signals to into digital form has brought a game-changing revolution in the field of communication. Modulation is the common term used in communication systems. Communication systems use modulation and Demodulation methods for effective transmission of low-frequency signals. When modulation is used along with digital signals it solved many drawbacks of analog communication. Some of the digital signal processing methods used in communication systems are Pulse code modulation, Differential pulse code modulation, Delta modulation, etc…

## What is Delta Modulation?

Delta modulation has its roots in Differential pulse code modulation method. It is also known as the simplified form of Differential pulse code modulation. Delta modulation is a scheme to permit the use of a simple quantizing strategy for constructing the encoded signals which are over-sampled purposely, to increase the correlation between adjacent samples of the signal, as seen in Differential pulse code modulation method.

This modulation is also called one bitter two-level version of Differential pulse code modulation. It provides a staircase approximation of over-sampled base-band signal. Here, the difference between the present sample and previous approximated sample is quantized into two levels i.e. ±δ.

If the previous approximation is below the present sample value, then the error is quantized by +δ. If the approximation is above the present sample value then the error is quantized by -δ.

### Delta Modulation Theory

Delta modulation is well-known for its simplicity. The basic principle of this technique can be formalized in three discrete-time relations as below-

1. e(nTs) = m(nTs) – mq (nTs – Ts )
2. eq(nTs) = δ sgn[e(nTs)]
3. mq(nTs) = mq(nTs – Ts) + eq(nTs)

where m(t) is the input signal and mq(t) is its staircase approximation. In the equations above, Ts is the sampling period, e(nTs) is an error signal representing the difference between the present sample value m(nTs) of the input signal and the latest approximation to it. eq(nTs) is the quantized version of e(nTs).

There are two types of quantizing errors that affect this Modulation system. They are the slope overload distortion and granular noise. Slope overload error occurs when the step size is too small relative to local slope characteristics of the input waveform. In contrast to slope overload error, granular noise occurs when step size is too large.

In this Modulation method, a larger step size leads to the accommodation of a wide dynamic range and small step size is required for the accurate representation of relatively low-level signals.

Thus, to compromise between slope overload distortion and granular noise errors, an optimum step size should be selected that can minimize the mean-square value of the quantizing error in a linear Delta modulator.

## Block Diagram

Delta modulation uses the over-sampling technique to achieve high signal-to-noise ratio. In delta modulation system, the transmitter circuit is composed of a Summer, Quantizer, Accumulator and an Encoder interconnected with each other.

Here, the integrator circuit contains a delay of Ts. The output of the integrator is a staircase approximation delayed by Ts. This staircase approximation is compared with the present sampled input signal at the summer and the difference gives the error signal.

This error signal is given to the quantizer circuit which consists of a hard limiter with an input-output relationship. Here, the error is quantized into two values i.e. ±δ. Then the output of the quantizer is coded to produce the desired Delta modulated wave.

At the receiver circuit, demodulation is done using an integrator and a low pass filter. The modulated wave is first decoded using a decoder and then the staircase approximation is reconstructed by  passing the positive and negative pulses produced at the decoder to the integrator.

The out-of-band quantizing noise in the high-frequency staircase waveform is removed by passing the signal through a low-pass filter whose bandwidth is equal to the original signal bandwidth.

Some of the advantages of Delta Modulation in comparison with other digital modulation techniques are given below-

• It was found that at lower bit rates Delta Modulation is better than the standard PCM. In a Delta modulation system, operating on voice signals under optimum conditions, the SNR is increased by 9dB by doubling the bit rate.
• The increase of SNR with bit rate is much more dramatic for Pulse code modulation than for Delta modulation. Therefore this modulation is recommended only in certain special circumstances such as when it is necessary to reduce the bit rate below 40 kilobytes per second and limited voice quality is tolerable.
• This modulation method is used if extreme circuit simplicity is of over-riding importance and the accompanying use of a high-bit rate is acceptable.
• Delta modulation works with lower channel bandwidth. This makes the system cost-effective and simple to implement. The feedback mechanism present in this Modulation system ensures the quick and robust delivery of data bits.

## Applications

Some of the applications of this modulation are given below –

• Voice transmission systems such as telephone and radio communications highly prefer this Modulation technique.
• Delta Modulation is most useful in systems where timely data delivery at the receiver is more important than the data quality.
• This modulation is applied to ECG waveform for database reduction and real-time signal processing.
• For analog-to-PCM encoding, this Modulation method is used.
• Delta Modulation is applied in television systems.

In this Modulation, there is a restriction on the amplitude of the input signal. In Delta Modulation only the error or the difference between the present sample and the previous sample is sent over the channel. In a case where there is no difference between samples, the modulated signal remains at the same 0 or 1 state of the previous sample. Some of the derived forms of delta modulation are Continuously Variable Slope Delta modulation, Delta-sigma modulation, and Differential modulation. Which is the superset of Delta Modulation?