Stepped Swept Sine -- Frequency & Timing Calculations

[John_Freeman]

I am attempting to generate a Stepped Swept Sine generator for use in doing a Shaker Controller.  I need to calculate the Time per Step and Frequency Increments to do a n-Octave/minute sweep with various sub-octave steps. For example 1/8th octave frequency steps, at 1/2 Octave per minute from 5Hz - 3KHZ.

Requirements:

1.)  Individual frequency durations must be such that the waveform starts and ends at zero volts so that the transition to the next frequency doesn't cause distortion. See Stepped Sine Example file attached.

2.)  I need calculate the nearest number of cycles to met the timing for step times.

3.)  It is my understanding that the timing for individual steps changes on some kind of logarithmic or exponential rate. In my example of 1/8th octave steps at 1/2 octave per minute the timing would not be simply 4 equal step times over a 1 minute period. Rather it changes for each frequency and to total duration of 4 steps would equal 1 minute.  I am struggling with calculating this timing.

4.) In addition, the frequency doesn't change linearly. It also changes on some kind of logarithmic or exponential rate.

The combination of #3 and #4 has me stumped. I have attached a couple of graphs showing the frequencies and time vs step. Also another graph showing an example Swept Sine Profile.

I know there is a function in the Sound & Vibration Toolkit but I am unable to afford it just to get this capability.   I have attached a couple of graphs showing

Any suggestions.

[johnsold]

I suggest that you take the time to do the math, or at least an approximation to start:

a. Start by calculating the desired frequencies. Get the periods for each of the frequencies. 

b. Determine the approximate times that each octave should end for the specified rate. Estimate the nominal time each frequency step should end.

c. Check to see how close the times in (b) are to integer multiples of the periods in (a).  The biggest discrepancies should occur at the low frequency end. 

d. Determine the minimum number of cycles required at the lowest frequency to provide satisfactory results with the shaken object.

f. Use the various constraints to "build" the swept sine signal. Start with the minimum number of cycles of the lowest frequency. At the time that segment ends repeat the process for the next frequency, except that both the minimum number of cycles and the nominal time for ending that frequency step (b) need to be considered. Continue.

The procedure described above will tend to run slower than the specified n-Octave/minute rate. If keeping close to the rate is important, it may be necessary to end some segments one or more cycles early, most likely at the higher frequencies. You and your client need to determine what compromises will be acceptable.

Lynn