the original waveform can be reconstructed with adequate precision. In contrast, without conversion to a pulse stream but simply transmitting the analog signal directly, all noise in the system would be added to the analog signal, reducing its quality. The use of PDM as a signal representation is an alternative to pulse-code modulation (PCM), sampling and quantizing to a multi-bit code at the Nyquist rate. Analog to digital conversion Description A delta-sigma or other pulse-density or pulse-frequency modulator generates a pulse stream in which the frequency, , of pulses in the stream is proportional to the analog voltage input, , so that , where is a constant for the particular implementation. A feedback loop monitors the integral of and when that integral has incremented by , which is indicated by the integral waveform crossing a threshold, , it subtracts from the integral of so that the combined waveform sawtooths between and . At each step a pulse is added to the pulse stream. A counter sums the number of pulses that occur in a predetermined period, , so that the sum, , is . In a given implementation, is chosen so that a digital display of the count, , is a display of with a predetermined scaling factor. Because may take any designed value, it may be made large enough to give any desired resolution or accuracy. Analysis For the purpose of introduction, Figure 1 illustrates the concept of voltage-to-frequency conversion, in an unclocked form that resembles delta-sigma modulation, and is called asynchronous modulation, asynchronous delta-sigma modulation, or free-running modulators. Shown below that are waveforms at points designated by numbers 1 to 5 for an input of 0.2 volts in the left column and 0.4 volts in the right column. The stream of delta impulses generated at each threshold crossing is shown at (2) and the difference between (1) and (2) is shown at (3). This difference is integrated to produce the waveform (4). The threshold detector generates a pulse (5) which starts as the waveform (4) crosses the threshold and is sustained until the waveform (4) falls below the threshold. The threshold (5) triggers the impulse generator to produce a fixed-strength impulse. The integral (4) crosses the threshold in half the time in the right column than in the left column. Thus the frequency of impulses is doubled. Hence the count increments at twice the speed on the right