Deltamodulation

Delta modulation, also referred to as Δ modulation or Δ -M is used to pulse-frequency modulation (PFM) and pulse density modulation (PDM ) is a variation of the differential pulse code modulation (DPCM ), wherein the pulse coded signal on the transmission channel, only the two states 0 and 1 accept and can be encoded by a bit. The pulse width of a single pulse or the duration of a bit is constant in time.

The procedure is used to convert an analog waveform into a digital signal. The larger the input signal to be converted, the more pulses of constant duration are generated per unit time. The method is related to the pulse width modulation (PWM), in which, however, the pulse width is varied at a constant frequency.

Delta modulation is used inter alia, in the measurement and control of switching regulators and DC-DC converters and generally referred to in this context as the pulse frequency modulation. In the field of signal processing, the same process is referred to as delta modulation and serves to analog waveforms in a binary sequence to implement. An extension of the delta modulation is the delta-sigma modulation ( ΣΔ ) modulation, which is used, inter alia, supplemented by digital filter for analog -to-digital converters ( ADCs ).

General

In delta modulation, the analog signal is sampled at uniform intervals, each sample is compared to a stored and the previous one. The second sample is greater than the first signal 1 is produced by the delta modulator. The second sample is smaller, a 0 signal is generated.

To achieve an appropriate dynamic range of the delta modulation, a higher sampling frequency than that of the pulse code modulation is used. It must be chosen to satisfy the Nyquist -Shannon sampling theorem as in the pulse code modulating at least one sampling frequency. This corresponds to the delta modulation of the dynamic range by one bit. In delta modulation, therefore, the sampling frequency is chosen to be significantly higher than this lower value, higher for a dynamic range of n bits by a factor of 2n, since it can lead to slope overload distortion else.

Mathematical Description

The pulse frequency modulation can be seen as a consequence of the values ​​{0, 1} are described. The logical value of a bit 1 is usually associated with the positive signal value A, the logic value 0 to the value -A. The two values ​​are the values ​​bipolar sequence xn which by the PFM and PDM is formed.

This makes it possible to express the bipolar pulse frequency modulation as:

Or

1 a sequence of constant values ​​results in a constant signal having the value A as a positive extreme value, a sequence of constant values ​​0 gives the constant signal to the negative extreme value -A. Signal values ​​between A and -A are formed by different sequences with different frequencies from the values ​​{0, 1}. By low-pass filtering the result can be xn form an analog waveform running.