Technique of reconstructing and displaying an analog waveform from a small number of magnitude samples

A method of acquiring and displaying an analog waveform, comprising the steps of:

• acquiring samples of the magnitude of said waveform at equal time intervals therealong,
• determining the slope of the waveform at a plurality of such samples, a method of determining each such slope for a given sample point comprising the steps of:
• determining the slope of a line extending between sample points immediately on either side of said given sample point,
• determining the slope of a line extending between sample points on either side of said given sample point and removed one sample therefrom,
• ratioing the two slopes,
• using the value of said ratio as an index to a table, thereby to give a value from said table, and
• multiplying the value from the table by the slope first determined above, thereby to obtain the value of the waveform slope at said given sample point, and
• utilizing said slopes to display information of said analog waveform.

A method of acquiring and displaying an analog waveform, comprising the steps of:

• acquiring samples of the magnitude of said waveform at equal time intervals therealong,
• determining the slope of the waveform at each of a plurality of successively acquired samples,
• determining the slope of the waveform at a point intermediate of each sampling interval, each intermediate slope being determined by a method comprising the steps of:
• determining the difference in magnitude of the acquired samples at the beginning and end of the interval and multiplying that difference by two, and
• determining the sum of the calculated slope of the curves at the acquired samples at the beginning and end of the interval, dividing such sum by two and subtracting the resulting quantity from that determined from the preceding step,
• determining the magnitude of a plurality of points within the sample intervals, the points within a given sample interval being determined in part from the magnitude of the determined intermediate slope, and
• displaying the sample magnitudes and the determined intermediate magnitudes in a manner to permit observation of a reconstructed waveform.

For an analog waveform wherein samples of its magnitude have been taken at equal time intervals therealong, a method of determining the frequency of said analog waveform at a given sample, comprising the steps of:

• determining the slope of the line extending between sample points immediately on either side of said given sample,
• determining the slope of the line extending between sample points upon either side of said given sample and removed one sample therefrom, ratioing the two slopes,
• determining the arc cosine of said ratio, thereby to give the sample interval in radians of the analog waveform, and
• converting the interval in radians to frequency and indicating said frequency.

A system for displaying an accurate replica of an analog waveform, comprising:

• means receiving said analog waveform for taking samples of its magnitude at equal time intervals therealong,
• means receiving said samples for determining the slope of the waveform at each of a plurality of successively acquired samples,
• means receiving the samples and the determined slopes thereat for estimating the slope at the waveform at a point intermediate of each sampling interval,
• means receiving the acquired samples, the determined slopes thereat and the estimated intermediate slopes for estimating the magnitude of a plurality of points within each of the sample intervals, and
• means receiving the acquired samples and the estimated sample points for creating a display of the reconstructed waveform.