Digital Circuit & ADC The advantages of digital technology: 1. less internal noise, 2. the ability to do complex operations in small ICs 3. include greater predictability of operation, 4. consume little power.
A. Analog-to-digital converters: 1. Analog-to-digital converter (ADC) → change the analog electrical voltage coming from the microphone into → numbers. 2. Sampling is the first step in this process → by noting the size of the signal at regular time intervals, and totally ignoring the value in-between these sampling points. 3. Quantization error (QE): Error resulting from trying to represent a continuous analog signal into discrete, stepped digital data. The problem arises when the analog value being sampled falls between two digital “steps.” So, the analog value must be represented by the nearest digital value, → resulting in a very slight error. 4. In other words, QE is, the difference between the continuous analog waveform, and the stair-stepped digital representation. 5. For a sine wave, QE will appear as extra harmonics in the signal. → as wideband noise → “Quantization noise” 6. Factors affecting QE: - dynamic range of ADC (is the largest voltage that can be accurately digitized) - number of bits of ADC. 7. Solution: to reduce quantization error: - the more bits the better, as HA will be able to handle a greater dynamic range of signals without adding excessive noise of its own. - reduce the ADC voltage range,
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- increase bioamplifier gain (as in evoked potential systems → bioamplifier amplifies the signal of interest so that it occupies most of the ADC voltage range, and in doing so we improve the amplitude resolution of our digital system). 8. Nyquist sampling theorem: the sampling rate should be at least twice the maximum frequency component of the signal of interest. In other words, the maximum frequency of the input signal should be less than or equal to half of the sampling rate. E.g. HA is to amplify signals up to, say, 10 kHz, the sampling frequency has to be at least 20 kHz. This means the waveform is sampled every 1/20,000 of a second, or every 50 ms (i.e. sampling period= 50 ms which is the inverse of sampling frequency = 20 kHz). 9. Any frequencies higher than the Nyquist frequency → Cause aliasing & erroneous results. 10. Anti-alias filter: Def: A low pass filter (a filter that passes low frequencies but attenuates the high frequencies) is added before the sampler and the ADC → attenuating the higher frequencies (greater than the Nyquist frequency), it prevents the aliasing components from being sampled. Because at this stage (before the sampler and the ADC) you are still in the analog world, the anti-aliasing filter is an analog filter. Or it may be an intrinsic part of the analog-to-digital conversion process. 11. An ideal anti-alias filter passes all the appropriate input frequencies (below f1) and cuts off all the undesired frequencies (above f1). However, such a filter is not physically realizable. In practice, filters look as shown in illustration (b) below. They pass all frequencies < f1, and cut-off all frequencies > f2. The region between f1 and f2 is known as the transition band, which contains a gradual attenuation of the input frequencies, the transition band could still cause aliasing. Therefore, in practice, the sampling frequency should be greater than two times the highest frequency in the transition band. So, this is more than two times the
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maximum input frequency (f1). That is one reason why you may see that the sampling rate is more than twice the maximum input frequency.
12. To avoid aliasing, it is wise to sample at two times the Nyquist rate (i.e., four times the highest frequency in the analog signal of interest) 13. The waveform would be represented by the numbers (called the code) → The sampled waveform has now been digitized. 14. Binary Number System:
In our base decimal number system, each place can represent 10 different values (0 through 9). In the base 2 or binary number system, each place can represent only two values: 0 or 1.
E.g. 25 can be described as: 25 = (2 × 10¹) + (5 × 10ᴼ)
Another example:
15. each of these binary places is referred as a bit, and hence 1100010 is a seven-bit binary number. The word bit is a contraction of the words binary digit. Because we need to convey negative and positive numbers, the numbers can be arranged so that the first bit represents the sign of the number.
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16. Why is it necessary to break the sampled values up into bits?
First, it is convenient for computers, because they can most efficiently represent signals as either on or off and these can easily be thought of as the two values of a binary digit.
Having only two values makes a signal almost incorruptible when it is stored, transmitted, or used in any way.
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Facilitates noise reduction, whereas in an analog signal the noise would be
mixed up with the signal and would pass to HA wearer. Note that this advantage applies only to noise generated internally within the digital part of HA, not noise picked up by the hearing aid or created within the microphone, pre-amplifier, or ADC. Once sound has been represented as a series of numbers, we can modify the
sound just by doing arithmetic with the numbers.
B. Digital signal processors: -
There are two types of digital signal processors used in HA:
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Hard wired and general arithmetic processor:
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Hard wired processor: -
in which different parts of the processor each perform some specific function (e.g. a compressor, or a filter).
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These blocks are connected together in a fixed order i.e. it can process sounds in only the way represented by that particular block diagram.
ii.
General arithmetic digital processing: -
As with a computer, it would do whatever its software told it to do.
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There is no fundamental limit to what HA of this type could do.
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Unfortunately, to date we have a fairly restricted list of things that we would like them to do,
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advantage: - could be updated by a new software without buying a new HA - super-flexible aid, in which the aid wearer can switch between different signal processing schemes (each with its own block diagram) using a remote control.
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General arithmetic processor hearing aids are sometimes described as open platform → because it is open to people other than the IC manufacturer to write software that will run on the IC.
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General arithmetic processors can contain hard-wired circuits to handle frequently repeated calculations in an efficient manner.
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Conversely, hard-wired processors can contain a small general arithmetic processor that can control how parts of a hard-wired circuit are configured. For some time, most digital hearing aids are likely to be a hybrid of hard-wired circuits and general arithmetic processors.
Signal Delay: -
Any delay in the amplified sound path, even including the very short delay found in analog HA → can disrupt the resulting gain-frequency response of the complete system for people with mild or moderate losses.
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The acoustic (non-delayed, via open fitting) and amplified (delayed) sound paths will partially cancel at particular frequencies but add constructively at frequencies intermediate to these. The resulting series of peaks and troughs in the frequency response is referred to as comb filtering.
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The greater the delay → the greater cancellation will occur.
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Delays of 5 ms to 10 ms may lead to equally acceptable sound quality. Delay increases beyond 10 up to 20 ms, → the sound quality decreases but may be tolerable.
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Some filtering methods delay low frequency sounds to a greater extent than high frequency sounds.
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when the low frequencies are delayed with respect to the high frequencies, differential delays as small as 5 ms can be detected. Delays around 10 ms are disturbing and delays of 15 ms affect the intelligibility of incoming speech.
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Longer delays of 40 ms or more put the auditory information out of synchronization with visual information and so may disturb lip-reading, particularly for good lip-readers.
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C. Digital-to-analog converters:
After the digital signal processor has altered the sound → the modified numbers must be converted into an acoustic signal. This conversion is the job of the digital-to-analog converter (DAC) combined with the receiver.
To minimize power consumption, digital HA use a different solution. The multiple bits that comprise each sample are converted into a single bit that changes at a rate many times higher than the sample rate. The converter is referred to as a digital-to-digital converter.
The high-speed serial output from this converter is fed to the receiver, which averages out the high-speed variations in the digital signal to produce a smooth analog signal. The digital-to-digital converter and the receiver thus combine to make up the digitalto-analog converter.
specifications affect the sound quality that HAs provide: 1. Instructions per second: - Digital processors are characterized by the number of instructions or operations that they can do in a second. A processor, for example, may be able to do 40 MIPS (million instructions per second). - ↑↑ the number of instructions per second, → ↑↑ current consumption → ↓↓ battery life. 2. Sampling rate: - describes how many times per second HA samples the input signal. - The major impact is that HA can amplify sounds only up to about 40 to 45% of the sampling frequency, with the absolute theoretical maximum being 50%. - A second impact is that if the sampling rate is unnecessarily high, the complexity of the processing that HA can perform will be unnecessarily limited. Consequently, fewer operations can be performed on each sample.
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3. Number of bits:
The greater the number of bits, the greater the number of analog voltage levels that we can represent.
Quantization Error: ------mentioned…
4. Current consumption:
The current consumption, and hence battery life and feasible battery size, depends on: * the instruction rate, * the voltage at which the integrated circuit operates, and * the technology used to make the integrated circuit.
5. Processing delay:
As mentioned in the previous section an excessive time delay from input to output of the hearing aid will degrade signal quality…
6. HA Physical size affected by transducers size & size of integrated circuit.
Digital vs analog hearing aids:
Digital HA required less power and volume than analog HA performing operations of similar complexity.
The only significant disadvantage of digital HA is the longer delay between the input and output as mentioned.
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