Waveform generation
A waveform generator for generating a smooth version of an original waveform which contains abrupt transitions, includes a phase accumulator incremented at successive sampling times to produce an output representative of the phase of the original waveform, a phase scaler arranged to convert the residual contents of the accumulator following a transition from phase to time, computing means responsive to the time to calculate a number of samples along a smooth transition, each offset by that time from the sampling times, and a sequencer to replace the otherwise abrupt transition with the sequence of samples from the computed smooth transition.
1. A waveform generator for generating a data stream comprising a plurality of data values at predetermined sample times, the data stream being representative of a smooth version of an original waveform, the original waveform including at least one abrupt transition, the waveform generator comprising:
a phase accumulator arranged to provide an output representative of the phase of the original waveform, the accumulator output being sequentially incremented by a predetermined increment value at successive sample times;
a transition detector arranged to receive the accumulator output and to provide an output signal when the accumulator output is at least equal to a value representative of the phase of the original waveform at the point of an abrupt transition;
a phase scaler arranged, in response to receiving the output signal from the transition detector, to determine from the accumulator output the difference between the phase represented by the accumulator output and the phase of the original waveform at the point of the abrupt transition and to convert the phase difference to a time value;
a data processor arranged to generate a sequence of data values representative of a smooth transition offset by the time value from the sample times; and
a sequencer arranged to insert said sequence of data values into said data stream.
2. A waveform generator according to claim 1 , wherein the data processor is arranged to calculate the sequence of data values representative of the smooth transition in accordance with the time value output from the phase scaler.
3. A waveform generator according to claim 1 , further comprising a data storage device having a plurality of predetermined sequences of data values stored thereon, each predetermined sequence of data values being representative of a smooth transition offset by a particular value of the time value output from the phase scaler, the data processor being arranged to select the predetermined sequence of data values corresponding to a particular time value that is closest in value to the time value output from the phase selector.
4. A waveform generator according to claim 1 , further comprising an offset generator arranged to receive the output from the phase accumulator, to sum the output value with a predetermined offset value and to provide the product of the summation to the transition detector, wherein the transition detector provides a further output signal representative of a further abrupt transition.
5. A waveform generator according to claim 1 , wherein said predetermined increment value is variable.
6. A waveform generator according to claim 1 , wherein the smooth transition corresponds substantially to a gaussian pulse response convolved with a square wave.
7. A waveform generator for generating a sequence of data values at predetermined time intervals, the sequence of data values being representative of a smooth version of an original waveform, the original waveform comprising periods of constant amplitude separated by abrupt transitions, the waveform generator comprising:
a phase accumulator arranged to provide an accumulator output the value of which is incremented by a predetermined value at each predetermined time interval, the accumulator output being representative of the phase of the original waveform;
a phase mapper arranged to receive the accumulator output and to generate a modified phase output in accordance with the received accumulator output; and
an output generator arranged to output a data value of said sequence of data values in accordance with the modified phase output received from the phase mapper.
8. A waveform generator according to claim 7 , wherein the output generator comprises a look-up table having a plurality of predetermined data values each corresponding to a modified phase output value.
9. A waveform generator according to claim 7 , wherein the phase mapper generates a constant modified phase output when the accumulator output is representative of a period of the original waveform having a constant amplitude and wherein said constant modified phase output corresponds to a single data value in the look-up table.
10. A waveform generator according to claim 7 , where the phase mapper comprises comparator means for comparing the accumulator output with one or more predetermined threshold values, the or each threshold value defining the boundary between said periods of constant amplitude in the original waveform.