The extra samples needed to produce a super high rate are interpolated from the recorded samples.īy the way, the circuits that generate the sample rate must be exceedingly accurate. Many systems now use a very high sample rate at the output in order to simplify the filters. Such filters are difficult and expensive to build. If the sampling rate is only twice the frequency of interest, the filters must have a very steep characteristic to allow proper frequency response and satisfactorily reject the sampling clock. (An identical filter should be placed before the ADC to prevent aliasing of any unsuspected ultrasonic content, such as radio frequency interference.) The extra junk must be removed with a low pass filter that cuts off a little higher than the highest desired frequency. A Fourier analysis of this would show that everything belonging in the signal would be there along with a healthy dose of the sampling rate and its harmonics.
Best value digital to audio converter series#
Figure 4 shows how the waveform improves as the sampling rate is increased.Įven at high sample rates, the output of the system is a series of steps. For best results, sampling rates twice or four times this should be used. The Nyquist rate (twice the frequency of interest) is the lowest allowable sampling rate.
(The mathematical statement of this is the Nyquist Theorem.) This implies that if we are dealing with sound, we should sample at least 40,000 times per second. The sampling rate must be greater than twice the frequency measured for accurate results. This can happen even if the sampling rate is twice the frequency of the input if the input is a sine or similar waveform. If the sampling rate were exactly the frequency of the input, the result would be a straight line, because the same spot on the waveform would be measured each time. If the sampling rate is lower than the frequency we are trying to capture, entire cycles will be missed, and the decoded result would be too low in frequency and might not resemble the proper waveform at all. The rate at which the numbers are generated is even more important than the number of bits used. Moving a binary number one space to the left multiplies the value by two (just as moving a decimal number one space to the left multiplies the value by 10), so each bit doubles the voltage that may be represented.ĭoubling the voltage increases the power available by 6 dB, so we can see the dynamic range available is about the number of bits times 6 dB.
The number of bits in the number also determines the dynamic range. Distortion in digital systems increases as signal levels decrease, which is the opposite of the behavior of analog systems. The distortion is roughly the percentage that the least significant bit represents out of the average value. If there are more bits in the number the waveform is more accurately traced, because each added bit doubles the number of possible values. If there were only one bit in the number, the ultimate output would be a pulse wave with a fixed amplitude and more or less the frequency of the input signal.
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