DSP Blockset

Example: Nonzero Tasking Latency.   Most multirate blocks experience tasking latency only in the Simulink multitasking mode. As an example, consider the following model.

To engage the Simulink multitasking mode, adjust the following settings in the Solver panel of the Simulation Parameters dialog box:

• Type = Fixed-step
• Mode = MultiTasking

Use the default settings for the Mux and To Workspace blocks. Adjust the other blocks' parameter settings as follows:

• Set the Signal From Workspace block's parameters to the values below.
• Signal = 1:100
• Sample time = 1/4
• Samples per frame = 4
• Set the Upsample block's parameters to the values below. The Maintain input frame size setting of the Frame-based mode parameter makes the block (and model) multirate since the input and output frame rates will not be equal.
• Upsample factor = 4
• Sample offset = 0
• Initial condition = -1
• Frame-based mode = Maintain input frame size
• Set the Sample time parameter of the Digital Clock block to 0.25 to match the sample period of the Upsample block's output.
• Set the Output signal parameter of the Frame Status Conversion block to Sample-based.

Notice that the current value of the Simulink timer (from the Digital Clock block) is prepended to each output frame. The frame-based signal is converted to a sample-based signal by the Frame Status Conversion block so that the output in the command window will be easily readable.

In the example, the Signal From Workspace block generates a new frame containing four samples once every second (T_fo = *4). The first few output frames are shown below:

• (t=0)   [ 1  2  3  4]
  (t=1)   [ 5  6  7  8]
  (t=2)   [ 9 10 11 12]
  (t=3)   [13 14 15 16]
  (t=4)   [17 18 19 20]
  

The Upsample block upsamples the input by a factor of 4, inserting three zeros between each input sample. The change in rates is confirmed by the Probe blocks in the model, which show a decrease in the frame period from T_fi = 1 to T_fo = 0.25.

Question: When does the first input sample appear in the output?

The "Latency and Initial Conditions" section of the reference page for the Upsample block indicates that when Simulink is in multitasking mode, the first sample of the block's frame-based input appears in the output as sample M_iL+D+1, where M_i is the input frame size, L is the Upsample factor, and D is the Sample offset. This formula therefore predicts that the first input in this example should appear as output sample 17 (i.e., 4*4+0+1).

To verify this, look at the output from the simulation, saved in the workspace array yout. To convert the array to a easier-to-read matrix format, type

• squeeze(yout)'
  

The first few samples of the result, ans, are shown below:

The first column of yout is the Simulink time provided by the Digital Clock block. The four values to the right of each time are the values in the output frame at that time. You can see that the first sample in each of the first four output frames inherits the value of the block's Initial conditions parameter. As a result of the tasking latency, the first input value appears only as the first sample of the 5th output frame (at t=1), which is sample 17.

Predicting Tasking Latency

Example: Zero Tasking Latency