## Need Help In Interpreting Curves in a Chart

Started by 6 years ago6 replieslatest reply 6 years ago150 views
In the most recent edition of the IEEE Sig. Proc. Magazine was an article discussing a new technique to perform sample rate change (SRC) [1]. The authors started out by presenting the following Figure 1 illustrating both the time-domain and frequency-domain methods for implementing a sample rate change on the input x(n) sequence.

Figure 1. The steps of SRC: (a) The time-domain method and (b) The frequency-domain method.

The topic of the article was the authors' "new, improved, and more accurate" algorithm to implement the center block in Figure 1(b) using a scheme they called "Calibrated frequency-domain SRC."  At the end of the article they presented the following Figure 5 showing the computational speed of their new "calibrated SRC" scheme compared to the computational speed of other SRC methods, for both decimation and interpolation, as implemented on a PC-compatible desktop computer.

The Legend in Figure 5 is interpreted as follows:

T-SRC (500) = SRC in Figure 1(a) using a 500-tap FIR filter.

T-SRC (300) = SRC in Figure 1(a) using a 300-tap FIR filter.

T-SRC (100) = SRC in Figure 1(a) using a 100-tap FIR filter.

F-SRC (Uncalibrated) = Figure 1(b) using a previously-published technique.

F-SRC (Calibrated) = Figure 1(b) using their proposed SRC method.

Figure 5. The computation time for time-domain SRC (T-SRC), uncalibrated, and calibrated frequency-domain SRC (F-SRC). (The x-axis are the lengths of various x(n) input sequences.)

Here are my questions: How do we interpret the y-axis label, "Time/s", in Figure 5?  Do you think the "Time/s" nomenclature simply means "time measured in seconds"?  If it does then Figure 5 seems to indicate that the authors' "F-SRC (Calibrated)" method takes 10,000 times longer to compute than a previously-published "F-SRC (Uncalibrated)" method!  That doesn't seem "reasonable" to me.

Another question: For decimation, if an input sequence is 64-samples in length what does it mean to pass a 64-sample x(n) sequence through a 500-tap FIR filter prior to downsampling?  Would the filter's output sequence have any meaning?  I look forward to any opinions from you guys here on dsprelated.com?

[1] L. Zhao, et al, "Autocalibrated Sampling Rate Conversion in the Frequency Domain", IEEE Signal Processing Magazine, May 2017, pp. 101–106.
[ - ]

It is time, in the paper they note that the "calibrated" requires more computation time but it increases performance (i.e. decreases MSE error - "significantly minimize conversion errors").  They state computational complexity for the calibrated is $$N^3$$ whereas the uncalibrated is $$NlogN$$.

[ - ]

Hi Chris.  So you're saying the y-axis in Figure 5 is simply time (seconds). OK. I'll buy that.  Yes, I saw the authors' words that "the computational complexity for the calibrated scheme is N^3 whereas the complexity of the uncalibrated scheme is N*(log base 10 of N).  When I compute those two complexity values for N = 64 I see a difference by a factor of 2,267 and not 10,000 as indicated in their Figure 5.  Oh well, I won't worry about that discrepancy.

My guess is that the proposed 'calibrated freq-domain SRC' scheme in not more accurate than traditional time-domain SRC schemes that use high-performance FIR filters. But(!), the 'calibrated freq-domain SRC' scheme is terribly more computationally intensive than an equivalent-perfomance time-domain SRC scheme. To me, the authors' method is not at all useful.  Of course, I may be wrong.

[ - ]

Rick,

That is a good point, I did not look at the full analysis in the article or the previous articles just looked up the plots after you posted the question.  In table 1 they state their method (calibrated) has the least error - I haven't reviewed their method to see if their approach is reasonable but it is the claim they make.

Regards,
Chris

[ - ]