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Powertran MCS1 (Part 1)

Playing with Time

MCS stands for MIDI Controlled Sampler, E&MM's most exciting build-it-yourself project yet. Tim Orr gets the ball rolling with a discussion of the effects this Powertran unit can be used to produce.

This issue sees the start of a series of articles describing the design and construction of the MIDI Controlled Sampler, E&MM's most advanced project ever. To kick things off, we present an in-depth analysis of the effects the MCS1 can generate and how they are used, plus an insight into the workings of digital audio.

MCS1 Design:
Tim Orr, R. Monkhouse, and Paul Bird
Editorial Presentation: Tim Orr

Put simply, the MCS1 is a digital sampling unit, though it is in fact capable of a great deal more than that description would suggest. Any sound can be stored within the unit's memory and played back via either a MIDI instrument or a one-volt-per-octave keyboard. The controlling keyboard determines the pitch of the reconstructed signal, thus making it possible for the user to make music from a single natural sound: pitch bend and vibrato effects can also be added as required.

A sophisticated looping system is used to turn sound endings into a sustained loop of infinite duration, and this allows the controlling keyboard to be played without the risk of 'running out' of sound due to lack of memory space. Sampled sounds can be stored on floppy disk for later retrieval.

Recordings can be made in free-running or auto-triggered modes, and on replay the sounds can be gated or triggered. Gated operation produces a sound output - including any loops - for as long as notes on the keyboard are depressed, while triggered operation requires only a start signal.

Sound-sampling is only one aspect of the MCS1's potential, however.

Figure 1. Typical music system employing all MCS control and memory options

The machine can also be used as a conventional digital delay line. It can be used to generate all the usual time delay effects such as phasing, flanging, vibrato, ADT and echo, and the theory and application of these effects will be discussed later. The available delay times range from a few milliseconds to tens of seconds, and other features include bypass, repeat, and infinite freeze functions. Memory size and sample speed are both continuously variable, while a pair of tracking filters takes care of anti-aliasing and recovery filter considerations, a software power clear ensures a quiet power-up, and a click-track is provided to aid timing during long sequences.

The MCS1 front panel incorporates 24 illuminated push-switches and a continuous rotary encoder to modify parameters, a four-digit 0.6" LED display indicating parameter information. Controls for level, repeat, mix and tune are also provided, along with a level indicator.

MCS1 memory size is variable from eight bytes to 64Kbytes: storage time at a 32kHz sampling rate is two seconds, while at 8kHz, the time is eight seconds, the longest possible replay time (for special effects) being 32 seconds. Eight-bit companding analogue-to-digital and digital-to-analogue converters are employed in the sampler's design, and the unit has an overall dynamic range of 72dB, audio bandwidth being variable from 12kHz to 300Hz. There are internal four-pole tracking filters for anti-aliasing and recovery, and a programmable wide-range sweep generator, generated in software.

Control range using a MIDI keyboard is five octaves, and using a one-volt-per-octave instrument, two octaves, though transposition can be employed in the latter case to provide a range of a further five octaves.

Figure 2. Some popular time delay effects
Figure 3. Phasing.
Figure 4. Flanging.
(Click image for higher resolution version)


Before going on to how the MCS1 itself works and how it can be built, it's worth devoting some time to how the various time delay effects it produces work out in theory. Figure 2 shows how these effects vary in their delay time.

Many of the effects commonly heard on today's modern music records are generated by manipulating natural sounds through a time delay unit. When a time delay is short, its effects are observed as frequency coloration, but longer delays move the effect out of the frequency domain and into the time domain. What follows is a guide to how these effects work.

Most phasing devices use an analogue allpass phase-shift circuit to generate a mobile comb filter, the number of notches commonly being between two and six. The same mobile comb filter can be simulated with a time delay unit such as the MCS1, the notch spacing being equal to the reciprocal of the delay time. Figure 3 shows how notch spacing expands and contracts with varying time delays, but what it doesn't show is that subjectively, phasing is quite a subtle effect, adding depth to the output of an electric guitar, for example.

Flanging was first heard on records in the late sixties and was initially generated by extending recording tape around the 'flange' of the play head (using something like a pencil), thereby producing a varying time delay which was then mixed with the undelayed signal. This technique produces a comb filter with lots of notches, which move in the frequency domain as the time delay is altered.

This effect - illustrated in Figure 4 - can be simulated relatively easily with a delay line, and by adding feedback, the filter response can be made excessively peaky, which gives modern-day flanging its characteristic tubular or 'drainpipe' sound coloration.

By varying the time delay with a sinewave modulator, a natural sound becomes frequency modulated, and modulation frequencies between 3Hz and 8Hz produce a standard vibrato effect: see Figure 5. Increasing the modulation depth causes something of an extreme effect, as does increasing the modulation frequency.

Short time delays in the order of 5-50mS can be used to simulate the addition of another instrument to the one being fed into the delay line. This effect comes off because when several instruments are being played together, perfect timing between their players is something of a rarity, to put it mildly. Since sound travels at about one-foot-per-millisecond, two instruments separated by a distance of ten feet may well be out of time by 10mS, though that delay is unlikely to be constant.

These effects are known in modern technological parlance as ADT (auto double tracking) and chorus, and delay lines can simulate this natural phenomenon quite easily - see Figure 6.

Natural reverberation, on the other hand, is a very complex phenomenon (Figure 7). Thousands of separate time delays and reflections conspire to achieve the final sound, but it is still possible to simulate their effects, even though the hardware required to do this is also complex. However, a simple reverberator can be constructed using a single time delay: using this method, the reverb is highly coloured and is often used on human speech to simulate a metallic or robotic quality.

Time delays greater than 50mS can be heard as distinct echoes. A short single echo is often used in modern music to provide a sharp 'slapback' sound, while longer echo times can be used with a little repeat to simulate Alpine echoes, for example.

More recently, time delays of the order of a few seconds have been widely used to build up sequences of rhythm tracks. To achieve this effect, the delay line's repeat control is kept fully on so that the inputted sound takes several trips around the loop before it disappears. On the MCS1, a click-track gives the user an audible indication of the loop's length, while a freeze function inhibits further writing to the memory so that the stored sound(s) can repeat indefinitely without any degradation in signal quality. The replay rate can then be altered to create dramatic pitch-shifting effects.

The effects described above can be applied to all common input signals and are available on a large number of digital delay lines from various manufacturers. However, the MCS1 adds a further dimension to effect manipulation by allowing the pitch of the unit's output to be controlled by an electronic keyboard.

The stored sound is transposed up or down in pitch by varying the replay rate, though the lower the replay pitch, the longer it takes for the sound to be reproduced. When a key is pressed on the controlling keyboard, reading starts from the beginning of memory and continues until either the key is released or the memory is exhausted, whichever is sooner. However, the MCS1 incorporates a looping facility that enables a continuous loop to be constructed at the end of a sound, giving it sustain for as long as a note on the keyboard is depressed. This method is widely employed by designers of electronic percussion units whose budget does not allow them to use ten EPROMs to store the sound of a cymbal! Figure 8 gives a graphic illustration of the looping process.

Figure 5. Vibrato.
Figure 6. ADT and Chorus.
Figure 7. Reverb.
(Click image for higher resolution version)

Digital Audio

In order for any audio signal to be stored in digital memory or held on a magnetic storage medium (eg. a floppy disk), it must first be converted into binary code. Once the signal has been digitally encoded, it can be stored and manipulated without any of the risks associated with analogue storage methods: noise does not accumulate, and the distortion level remains constant when the audio data is transferred from one unit to another.

A typical digital audio system is shown in Figure 9, where the sample and hold unit is used to freeze the input signal so that the ADC can perform a conversion on a static signal. The low-pass filter removes out-of-band frequency components after both stages of conversion have taken place. The audio signal is converted into a stream of digital information by the ADC (analogue-to-digital converter) and is then re-converted into an audio signal by the DAC (digital-to-analogue converter, simple isn't it?)

How do these converters work?

Well, think of the ADC as a sort of rapid digital voltmeter that measures the magnitude of the input voltage at regular time intervals. Each time it completes a measurement (the process is known as 'performing a conversion') it outputs a binary word representing the magnitude of the input voltage at that point in time. If the binary word is eight bits wide, the converter is capable of resolving the input voltage into 256 (2 to the power of 8) individual levels. The resolution of an ADC is proportional to the size of the binary word it produces, so that, for example, a 12-bit system has a resolution of one part in 4096 and a 16-bit system has a resolution of one part in 65,536.

The DAC is then used to convert the binary words back into an analogue voltage, and because the voltage is directly proportional to the magnitude of the binary code, the bit size of the DAC determines the number of separate voltage levels. However, the DAC's output is only a 'square wave' approximation to the original analogue input (which can move up and down smoothly) and this effect is known as quantisation - the digital equivalent of distortion, shown in Figure 10. Its effect can be reduced by increasing the bit size of the system as a whole, but as is the way of things, this invariably increases the system cost.

Figure 8. Sustaining a sound by turning a single cycle into a loop.
Figure 9. Digital Audio.
Figure 10. Quantisation distortion.
Figure 11. Recovering a sampled signal with a low-pass filter.
Figure 12. The sampling process generating a difference frequency.
(Click image for higher resolution version)

When we digitise an audio signal, we sample it at regular intervals of time, and in doing this, we define the time-varying shape of the signal as a series of points. By joining up these points (this is accomplished by the DAC) we can reconstruct the original signal. But how often should the signal be sampled, and does the sampling rate affect the system bandwidth? The answers to these questions lie in sampling theory. This states that a sinusoid defined by only two samples is recoverable, which in turn implies that the system bandwidth can be as much as half the sample frequency. In practice, however, the bandwidth is usually limited to about one-third of the sample frequency, due to filter limitations.

If a signal is sampled at a frequency of less than twice the signal bandwidth, there's a chance of frequency domain distortion - or 'aliasing' - taking place. Consider the sinewave being sampled at a frequency less than its own, as in Figure 12. The sampling process is meant to result in the original signal being recovered, but what is generated instead is a difference frequency. The resultant sound is something akin to ring modulation or detuned SSB reception, ie. very disturbing when applied to complex signals such as music or speech.

However, aliasing can be prevented by bandlimiting the input signal to one-half of the sample frequency using a good low-pass filter, which merely removes the signals that would cause aliasing products.

Figure 13. Aliasing.
(Click image for higher resolution version)

There's always a temptation to slow down the conversion frequency so that long time delays can be obtained from a fixed memory size, so it has become a practical necessity to incorporate a tracking low-pass filter in the design of some delay line products. The low-pass filter that precedes the ADC is known as the anti-aliasing filter.

In the first graph in Figure 13, the shaped area represents the power density spectrum of a typical audio signal, while the second drawing shows the same spectrum sampled at a frequency of Fs. Note that the lower sideband has an inverted spectrum and that the sideband pairs repeat at integer multiples of Fs. In the third diagram, the sample frequency has been reduced to 2 x FA, and the lower sideband is close to the audio base band: as a result, the system is on the verge of generating aliasing components. Finally, the fourth graph shows what happens when the sample frequency is reduced below 2 x FA. The low-pass filter is now allowing frequency components which generate aliasing signals to pass through, and aliasing begins.

Figure 14. Quantisation noise.
(Click image for higher resolution version)

Quantisation Noise

This phenomenon is caused by the inability of digital components to reproduce an arbitrary analogue signal accurately: a smooth analogue signal is presented to the ADC at the start of the process, but a crunchy output signal is reproduced by the DAC at the end of it. We can use distortion measuring techniques, normally used to measure THD (total harmonic distortion) in linear amplifiers, to examine quantisation noise. Figure 14 demonstrates the effect of quantisation.

Generally speaking, quantisation distortion has the spectral properties of noise. Because there is no simple integer relationship between the input signal and the sample frequency, the quantisation distortion bears no simple relationship to the input signal and therefore sounds noise-like.

Now, if a 1kHz sinewave were sampled 20 times faster at 20kHz, the resulting output would contain no quantisation noise as such, because the quantisation distortion would always be in the same place on each cycle of the sinewave and would therefore be heard as harmonic distortion.

A linear converter has quantisation levels at fixed, linearly-spaced intervals, and the best signal-to-quantisation noise ratio for a linear converter is given by the formula S/QN = (N x 6)dB, where N is the bit size of the converter. Thus, an eight-bit converter has quantisation noise 48dB below the maximum signal level. When the maximum signal level is only a quarter of the maximum, the ratio is poorer by 12dB, falling to 36dB, and if the input signal is so small that only the LSB (least significant bit) of the code is changing, then the S-to-QN ratio is only 6dB! However, when the input signal is so small that no bits are changing at all, then no quantisation noise is generated, thus proving that the process is a distortion mechanism rather than a noise one.

Figure 15. Companding.
Figure 16. Pre-emphasis noise reduction.
(Click image for higher resolution version)

Dynamic range is the ratio of the biggest signal level divided by the smallest the converters can handle. For linear converters, the dynamic range is represented by the S-to-QN ratio, or 48dB for an eight-bit system. If the quantisation levels are logarithmically spaced, ie. with small step sizes for low signal levels and large step sizes for higher ones, a somewhat larger dynamic range can be obtained. This is illustrated in Figure 15.

The DAC88 used in the MCS1 has a dynamic range of 72dB, and the log law is used to compress the signal at the ADC and expand it again at the DAC. For obvious reasons, this form of converter is known as a companding device, and is well suited to handling natural sounds such as speech and music, which require a large dynamic range if they are to be reproduced with any realism. However, it should be remembered that whenever an improvement is made to the dynamic range, quantisation distortion is invariably made worse.

Some of the effects of the degradation caused by quantisation distortion can however be masked by using a frequency pre-emphasis before the ADC and an equal (but opposite) de-emphasis after the DAC. This principle is shown in Figure 16.

How does it work? Well, because the spectral energy of sound rolls off with increasing frequency, it's possible to add high-frequency lift without running into any clipping problems, though if the sounds being processed are a little on the bright side, the system has to be run at a lower operating level.

That about wraps up the theory side of digital audio and the effects that can be generated by digital delay lines: I hope what we've discussed has cleared up a few grey areas that might have existed in some people's minds, as well as providing some 'food for thought' for budding designers and constructors. Next month, we'll take a closer look at the MCS1's circuit operation.

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Series - "Powertran MCS1"

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Powertran MCS1

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