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RobertZ

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the art of analog

Posts: 55
San Diego, CA

Fourier analysis and DFT compare
May 20^th, 2007, 11:33pm

Hi,

I did two simulations using ideal 10 bits ADC and DAC, and check the spectrum at the ideal DAC output.
1st one, fclk = 32MHz, fsig = 1MHz, DFT and Fourier analysis results match each other.
2nd one, fclk = 32MHz, fsig = 0.96875MHz. The Fourier analysis using the last period (38.9677us ~ 40us) to find the fourier coefficients. If I use the same period for DFT, the results match, as expected. If I use 8us to 40us to do DFT, which is exactly 31 periods (32us length), the DFT result shows less magnitude at harmonics. I would trust the DFT result more for the 2nd case. Any one can comment on this?

Thanks!

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Thanks,
Robert

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sheldon

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Posts: 751

Re: Fourier analysis and DFT compare
Reply #1 - May 23^rd, 2007, 4:47am

Driveforce,

Some comments:

1) You using a fourier command like
FOUR0 ( out 0) fourier fund=968710.6461 harms=??

As mentioned in one of the previous appends, it would be better
to add the normharm property to the symbol

FOUR0 ( out 0) fourier fund=31250 harms=1024 normharm=31

This will allow a direct comparison of the DFT and Fourier analysis
results. Currently the analysis use different fundemental frequencies.

2) The period appears to be a little off, (31/1024)*32MHz = 968750Hz,
1/(40us-39.9677us)=968710.6461 Hz and this could result in spectral
leakage that requires windowing. The Fourier component does not
include a windowing function so you need to be careful about frequency
selection.

3) An ideal DAC has quantitazation noise not distortion harmonics so you
need to compare snr ( or sinad) in order to verify the results.

4) For non-ideal DACs, the results would not be expected to match since
the DFT samples the waveform, i.e., that is it is difficult to capture the
the effect of glitch impulse on the response. The Fourier component
integrates over the waveform and is more suited for this measurement.

Best Regards,

Sheldon

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RobertZ

Community Member

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the art of analog

Posts: 55
San Diego, CA

Re: Fourier analysis and DFT compare
Reply #2 - May 23^rd, 2007, 5:17pm

Hi, Sheldon,

Thanks for your reply.

1) I didn't use fourier command, and don't know hwo, instead, I use fourier analysis in GUI, as shown in the following. The plus terminal should be connected output, not ground.
2) the period is automaticlly set by the fourier analysis. At the end of the analysis, it showed 307.434 m% mismatch between period begins and ends. �ls this causing spectrum leakage?

Thanks.

========================
Fourier Analysis `FOUR0'
========================

Fundamental frequency = 968.75 kHz.
Fundamental period = 1.03226 us.

Fourier components of V(net016) for the interval from 8.96774 us to 10 us:
DC = 412.951 mV.

Harm: �Absolute �Absolute �Relative �Relative
Magnitude Phase � � Magnitude Phase
� 1: �412.944 mV � � -95.4565 Deg � � 0.000 dB �0 Deg <- normalizer
� 2: �245.753 uV � � -155.438 Deg � �-64.508 dB -59.9814 Deg
� 3: �154.551 uV � � -127.679 Deg � �-68.536 dB -32.2226 Deg
� 4: �136.333 uV 70.9494 Deg � �-69.626 dB 166.406 Deg
� 5: �167.488 uV 127.225 Deg � �-67.838 dB 222.682 Deg
� 6: �70.1281 uV 50.7072 Deg � �-75.400 dB 146.164 Deg
� 7: �143.164 uV � � -4.80259 Deg � �-69.201 dB 90.654 Deg
� 8: �85.7771 uV � � -167.751 Deg � �-73.650 dB -72.2944 Deg
� 9: �57.4369 uV 85.7145 Deg � �-77.134 dB 181.171 Deg
�10: �58.2287 uV 58.7229 Deg � �-77.015 dB 154.179 Deg
�11: �96.982 uV -140.591 Deg � �-72.584 dB -45.1347 Deg
�12: �112.673 uV � � -151.425 Deg � �-71.281 dB -55.9682 Deg
�13: �48.6384 uV � � -81.8236 Deg � �-78.578 dB 13.633 Deg
�14: �73.3771 uV 139.605 Deg � �-75.007 dB 235.062 Deg
�15: �95.3559 uV � � -131.078 Deg � �-72.731 dB -35.6217 Deg
�16: �75.5083 uV � � -27.9219 Deg � �-74.758 dB 67.5347 Deg
�17: �27.7394 uV 40.3701 Deg � �-83.456 dB 135.827 Deg
�18: �10.836 uV 114.367 Deg � �-91.620 dB 209.823 Deg
�19: �29.4197 uV 24.4814 Deg � �-82.945 dB 119.938 Deg
�20: �75.3786 uV 78.4791 Deg � �-74.773 dB 173.936 Deg
�21: �40.8751 uV 159.28 Deg � � -80.089 dB 254.737 Deg
�22: �88.73 uV �12.2185 Deg � �-73.356 dB 107.675 Deg
�23: �58.7199 uV 111.711 Deg � �-76.942 dB 207.168 Deg
�24: �96.3994 uV � � -151.858 Deg � �-72.636 dB -56.4017 Deg
�25: �65.5622 uV � � -14.3222 Deg � �-75.985 dB 81.1343 Deg
�26: �56.5478 uV 63.265 Deg � � -77.270 dB 158.721 Deg
�27: �110.388 uV � � -157.099 Deg � �-71.459 dB -61.6427 Deg
�28: �87.8713 uV � � -56.0377 Deg � �-73.441 dB 39.4189 Deg
�29: �127.44 uV 70.3307 Deg � �-70.212 dB 165.787 Deg
�30: �193.419 uV 173.36 Deg � � -66.588 dB 268.817 Deg
Total harmonic distortion = 138.224 m% (-57.1883 dB).
RMS value of computed spectrum (excluding DC) = 412.945 mV.
RMS value of computed spectrum (including DC) = 583.996 mV.
Nonperiodicity (first/last point mismatch) = -1.26953 mV (-307.434 m%)

sheldon wrote on May 23^rd, 2007, 4:47am:

Driveforce,

� Some comments:

1) You using a fourier command like
� � FOUR0 ( out 0) �fourier fund=968710.6461 �harms=??

� �As mentioned in one of the previous appends, it would be better
� �to add the normharm property to the symbol
�
� �FOUR0 ( out 0) �fourier fund=31250 harms=1024 �normharm=31

� �This will allow a direct comparison of the DFT and Fourier analysis
� � results. Currently the analysis use different fundemental frequencies.

2) The period appears to be a little off, (31/1024)*32MHz = 968750Hz,
� �1/(40us-39.9677us)=968710.6461 Hz and this could result in spectral
� �leakage that requires windowing. The Fourier component does not
� �include a windowing function so you need to be careful about frequency
� �selection.

3) An ideal DAC has quantitazation noise not distortion harmonics so you
� �need to compare snr ( or sinad) in order to verify the results.

4) For non-ideal DACs, the results would not be expected to match since
� �the DFT samples the waveform, i.e., that is it is difficult to capture the
� �the effect of glitch impulse on the response. The Fourier component
� �integrates over the waveform and is more suited for this measurement.

Best Regards,

� Sheldon

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fourier.JPG

Thanks,
Robert

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venki_vlsi

Junior Member

Offline

Posts: 29
warangal

Re: Fourier analysis and DFT compare
Reply #3 - May 23^rd, 2007, 6:30pm

hi drive force,
i too using the same method(fourier compnent in GUI) in calculating distortion.
For Fs=125MHZ Nc=83,Ns=1024, i got Fin=10.1318Mhz
Since my Nc=83,i have to run my simulation for 83 clcok cycles(83*(1/10.1318M=8.192u ) with trans=0 to 8.192us.
I am getting good sfdr.but problem is with distortion and non periodic �mismatch.
any commnets on these how to improve.

========================
Fourier Analysis `FOUR1'
========================

Fundamental frequency = 10.1318 MHz.
Fundamental period = 98.6991 ns.

Fourier components of V(OU) for the interval from 8.0933 us to 8.192 us:
DC = 495.933 mV.

Harm: �Absolute � � � �Absolute � � � �Relative � � � �Relative
� � � Magnitude � � � Phase � � � � � Magnitude � � � Phase
� 1: �494.736 mV � � -105.375 Deg � � 0.000 dB � � � �0 Deg <- normalizer
� 2: �4.28339 mV � � -174.911 Deg � �-41.252 dB � � �-69.5364 Deg
� 3: �5.55389 mV � � �178.646 Deg � �-38.996 dB � � � 284.021 Deg
� 4: �5.43339 mV � � -170.83 Deg � � -39.186 dB � � �-65.4553 Deg
� 5: �5.19213 mV � � -171.569 Deg � �-39.581 dB � � �-66.1937 Deg
� 6: �5.68695 mV � � -168.216 Deg � �-38.790 dB � � �-62.8415 Deg
� 7: �6.41957 mV � � -166.124 Deg � �-37.737 dB � � �-60.7492 Deg
� 8: �7.52246 mV � � -160.438 Deg � �-36.360 dB � � �-55.0634 Deg
� 9: �9.12129 mV � � -158.374 Deg � �-34.686 dB � � �-52.9991 Deg
Total harmonic distortion = 3.61018 % (-28.8494 dB).
RMS value of computed spectrum (excluding DC) = 495.058 mV.
RMS value of computed spectrum (including DC) = 700.737 mV.
Nonperiodicity (first/last point mismatch) = 78.125 mV (15.7913 %).

Total time required for tran analysis `tran' was 1.18 s.

finalTimeOP: writing operating point information to rawfile.

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s.venkat_nitw

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RobertZ

Community Member

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the art of analog

Posts: 55
San Diego, CA

Re: Fourier analysis and DFT compare
Reply #4 - May 23^rd, 2007, 9:59pm

Hi, venki_vlsi,

Why did you get 15.7913% mismatch?
Did you using real circuit or ideal block?

By the way, Fin = 10.1318MHz may not be accurate enough for your calculation.

venki_vlsi wrote on May 23^rd, 2007, 6:30pm:

hi drive force,
i too using the same method(fourier compnent in GUI) in calculating distortion.
For Fs=125MHZ Nc=83,Ns=1024, i got Fin=10.1318Mhz
Since my Nc=83,i have to run my simulation for 83 clcok cycles(83*(1/10.1318M=8.192u ) with trans=0 to 8.192us.
I am getting good sfdr.but problem is with distortion and non periodic �mismatch.
any commnets on these how to improve.

========================
Fourier Analysis `FOUR1'
========================

Fundamental frequency = 10.1318 MHz.
Fundamental period = 98.6991 ns.

Fourier components of V(OU) for the interval from 8.0933 us to 8.192 us:
DC = 495.933 mV.

Harm: �Absolute � � � �Absolute � � � �Relative � � � �Relative
� � � Magnitude � � � Phase � � � � � Magnitude � � � Phase
� 1: �494.736 mV � � -105.375 Deg � � 0.000 dB � � � �0 Deg <- normalizer
� 2: �4.28339 mV � � -174.911 Deg � �-41.252 dB � � �-69.5364 Deg
� 3: �5.55389 mV � � �178.646 Deg � �-38.996 dB � � � 284.021 Deg
� 4: �5.43339 mV � � -170.83 Deg � � -39.186 dB � � �-65.4553 Deg
� 5: �5.19213 mV � � -171.569 Deg � �-39.581 dB � � �-66.1937 Deg
� 6: �5.68695 mV � � -168.216 Deg � �-38.790 dB � � �-62.8415 Deg
� 7: �6.41957 mV � � -166.124 Deg � �-37.737 dB � � �-60.7492 Deg
� 8: �7.52246 mV � � -160.438 Deg � �-36.360 dB � � �-55.0634 Deg
� 9: �9.12129 mV � � -158.374 Deg � �-34.686 dB � � �-52.9991 Deg
Total harmonic distortion = 3.61018 % (-28.8494 dB).
RMS value of computed spectrum (excluding DC) = 495.058 mV.
RMS value of computed spectrum (including DC) = 700.737 mV.
Nonperiodicity (first/last point mismatch) = 78.125 mV (15.7913 %).

Total time required for tran analysis `tran' was 1.18 s.

finalTimeOP: writing operating point information to rawfile.

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Thanks,
Robert

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venki_vlsi Junior Member Offline Posts: 29 warangal	Re: Fourier analysis and DFT compare Reply #5 - May 23^rd, 2007, 10:23pm hi .. its for actual ckt only. Can u plz tell me how to improve non-periodic mismatch. I tired to improve distortion to 44 db not more than that.my spec is 55 db.
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RobertZ

Community Member

Offline

the art of analog

Posts: 55
San Diego, CA

Re: Fourier analysis and DFT compare
Reply #6 - May 24^th, 2007, 12:00am

What is your clock frequency?
I ran a simulation with fclk = 125MHz, fin = 10.1318MHz. The fourier analysis shows no periodic mismatch.

========================
Fourier Analysis `FOUR0'
========================

Fundamental frequency = 10.1318 MHz.
Fundamental period = 98.6991 ns.

Fourier components of V(net016) for the interval from 9.9013 us to 10 us:
DC = 413.282 mV.

Harm: Absolute Absolute Relative Relative
Magnitude Phase Magnitude Phase
1: 409.473 mV -104.721 Deg 0.000 dB 0 Deg <- normalizer
2: 660.32 uV 155.756 Deg -55.849 dB 260.477 Deg
3: 387.222 uV 32.5348 Deg -60.485 dB 137.256 Deg
4: 544.762 uV -81.4079 Deg -57.520 dB 23.3131 Deg
5: 706.288 uV -167.658 Deg -55.265 dB -62.9373 Deg
6: 1.01321 mV 88.3409 Deg -52.131 dB 193.062 Deg
7: 988.561 uV -16.361 Deg -52.344 dB 88.36 Deg
8: 1.39653 mV -119.413 Deg -49.344 dB -14.6925 Deg
9: 2.32906 mV 132.577 Deg -44.901 dB 237.299 Deg
Total harmonic distortion = 801.097 m% (-41.9263 dB).
RMS value of computed spectrum (excluding DC) = 409.487 mV.
RMS value of computed spectrum (including DC) = 581.792 mV.
Nonperiodicity (first/last point mismatch) = 0 V (0 %)

[quote author=venki_vlsi link=1179729208/0#3 date=1179970201]hi drive force,
i too using the same method(fourier compnent in GUI) in calculating distortion.
For Fs=125MHZ Nc=83,Ns=1024, i got Fin=10.1318Mhz
Since my Nc=83,i have to run my simulation for 83 clcok cycles(83*(1/10.1318M=8.192u ) with trans=0 to 8.192us.
I am getting good sfdr.but problem is with distortion and non periodic �mismatch.
any commnets on these how to improve.

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Thanks,
Robert

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venki_vlsi Junior Member Offline Posts: 29 warangal	Re: Fourier analysis and DFT compare Reply #7 - May 24^th, 2007, 12:18am hi Drive force. Thanks a lot. What is simulation time?I ran from 0-8.192us..Its basically 83 intergercycles. Its looks u run more than 83 cycles from dats u have copied. How r u choosing simulation time? regards venkats
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RobertZ

Community Member

Offline

the art of analog

Posts: 55
San Diego, CA

Re: Fourier analysis and DFT compare
Reply #8 - May 24^th, 2007, 12:46am

at first, I ran simulation with ideal blocks.
The simulation time is 10us. For your case, real circuits, you may want to run more than 10us, since it need some time to settle down. Maybe that's the reason you had periodic mismatch.
But no matter how long the simulation time, fourier analysis automatically chooses the last fundamental period to do calculation.

Again, what is your clock frequency?

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Thanks,
Robert

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venki_vlsi

Junior Member

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Posts: 29
warangal

Re: Fourier analysis and DFT compare
Reply #9 - May 24^th, 2007, 1:07am

Hi,
My clock frequency is 125Mhz.

I understood where i went wrong.
previously i tried with dc voltage of 1.65 and amplitude of 1.65 to input sinewave so,i am getting nonperiodic mismatch.
now i tried with dc voltage of 0 and amplitude of 3.3v,i am not getting any non periodic mimsmatch but distortion is less when compared with previous case.

sorry for my english.

thanks driveforce.

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s.venkat_nitw

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sheldon

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Posts: 751

Re: Fourier analysis and DFT compare
Reply #10 - May 24^th, 2007, 3:25am

Venki,

Not sure that the dc level matters since the Fourier component
accounts for it. Here is the setup for your case.

NOTE:
To avoid accuracy issues, my testbench uses design variables:
numPoints --> number of points in the FFT, 1024
tones --> input signal tone, 83
fsample --> sample rate, 125M

so the Fourier component
fundamental frequency ==> fsample/numPoints
number of harmonics ==> numPoints/2
normharm ==> tone

This minimizes setup since all the variables are controlled from ADE,
makes the testbench re-usable, and eliminates the accuracy issue.

Best Regards,

Sheldon

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fourier_fft.pdf

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RobertZ

Community Member

Offline

the art of analog

Posts: 55
San Diego, CA

Re: Fourier analysis and DFT compare
Reply #11 - May 24^th, 2007, 11:35am

Sheldon,

I understand what your normharm means now.
But I couldn't find where to set it. My Fouier analysis always takes fundamental frequency as normalizer.

Here is the what I found in the netlist.
FOUR0 (net016 0) fourier fund=125M/1024 points=300 active=yes order=2 \
harms=512 refharms=83 scale=1

and the analysis print out likes this:
========================
Fourier Analysis `FOUR0'
========================

Fundamental frequency = 122.07 kHz.
Fundamental period = 8.192 us.

Fourier components of V(net016) for the interval from 1.808 us to 10 us:
DC = 412.985 mV.

Harm: Absolute Absolute Relative Relative
Magnitude Phase Magnitude Phase
1: 24.0204 uV -28.2579 Deg 0.000 dB 0 Deg <- normalizer
2: 12.7912 uV -122.369 Deg -5.473 dB -94.1112 Deg
3: 32.1999 uV -170.419 Deg 2.545 dB -142.161 Deg
4: 23.918 uV 42.1886 Deg -0.037 dB 70.4465 Deg
....

81: 37.8771 uV 98.2271 Deg 3.956 dB 126.485 Deg
82: 48.8834 uV -54.2941 Deg 6.172 dB -26.0361 Deg
83: 409.158 mV -104.695 Deg 84.626 dB -76.4374 Deg
84: 24.6046 uV 76.1291 Deg 0.209 dB 104.387 Deg
85: 46.3879 uV -93.9173 Deg 5.716 dB -65.6594 Deg

....

2nd question, how do you plot the fourier analysis output. It is only printed out into the output.log file.
3rd question, how do you use the window function? I only know the window function is availbe if I do FFT.

Thanks a lot!

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Thanks,
Robert

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venki_vlsi

Junior Member

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Posts: 29
warangal

Re: Fourier analysis and DFT compare
Reply #12 - May 24^th, 2007, 7:40pm

hi..
i too have used same test bench but we differ in giving values to fourier component.
can u clear me doubts in ur fourier component setup.
1.fundamental frequency ==> fsample/numPoints.
(I have given fin(10.1318Mhz) as fundemental frequency in fourier component.can u plz clear me why we should we use fundemental as fsample/number of points).
2.number of harmonics � ==> numPoints/2
(i have not mentioned any hormonic number in fourier component.its default showing 10 hormonics.I feel higher order hormonics doesnt effect much.Should we take 512 as default number in fourier componenet).
3.rmharm ==> tone
( i have not mentioned any refernce hormonic as i didnt understood what it means. can u give me little more details).

i too have done simulation with ur setup and results r getting differed.can u plz have a look.

========================
Fourier Analysis `FOUR1'
========================

Fundamental frequency = 122.07 kHz.
Fundamental period = 8.19202 us.

Fourier components of V(OU) for the interval from 1.80798 us to 10 us:
DC = 498.416 mV.

Harm: �Absolute � � � �Absolute � � � �Relative � � � �Relative
� � � Magnitude � � � Phase � � � � � Magnitude � � � Phase
� 1: �19.2405 uV � � -4.53968 Deg � � 0.000 dB � � � �0 Deg <- normalizer
� 2: �8.87069 uV � � -151.694 Deg � �-6.725 dB � � � -147.154 Deg
� 3: �64.5489 uV � � �96.2625 Deg � � 10.513 dB � � � 100.802 Deg
� 4: �9.9571 uV � � �-112.919 Deg � �-5.722 dB � � � -108.38 Deg
......
508: �39.9502 uV � � �18.8854 Deg � � 6.346 dB � � � �23.4251 Deg
509: �75.2377 uV � � -160.875 Deg � � 11.844 dB � � �-156.335 Deg
510: �14.0832 uV � � �127.099 Deg � �-2.710 dB � � � �131.639 Deg
511: �8.52414 uV � � -68.0349 Deg � �-7.071 dB � � � -63.4953 Deg
512: �5.03811 uV � � �162.856 Deg � �-11.639 dB � � � 167.395 Deg
Total harmonic distortion = 2.5702 M% (88.1994 dB).
RMS value of computed spectrum (excluding DC) = 494.52 mV.
RMS value of computed spectrum (including DC) = 702.117 mV.
Nonperiodicity (first/last point mismatch) = 0 V (0 %).

if u observe clearly my normaliser point is at 1st hormonic and ur normaliser point is at 83 hormonic.How ru able to acheive at that point)
these results r with setup as shown in fig.

Thanks and regards
venkat

sheldon wrote on May 24^th, 2007, 3:25am:

Venki,

� Not sure that the dc level matters since the Fourier component
accounts for it. Here is the setup for your case.

NOTE:
To avoid accuracy issues, my testbench uses design variables:
numPoints --> number of points in the FFT, 1024
tones �--> input signal tone, 83
fsample � �--> sample rate, 125M

so the Fourier component
fundamental frequency ==> fsample/numPoints
number of harmonics � ==> numPoints/2
normharm ==> tone

This minimizes setup since all the variables are controlled from ADE,
makes the testbench re-usable, and eliminates the accuracy issue.

� Best Regards,

Sheldon �

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653476535565364.jpg

« Last Edit: May 25^th, 2007, 12:52am by venki_vlsi »

s.venkat_nitw

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RobertZ Community Member Offline the art of analog Posts: 55 San Diego, CA	Re: Fourier analysis and DFT compare Reply #13 - May 24^th, 2007, 11:18pm Hi, venki, you should look at tone 83, which is your signal position, and your signal's harmonics are at 83x2, 83x3.... Sheldon's idea is very clever. setting fundamental equal to fsample gives long window (8.192u), which is also what you want. regards, driveforce
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venki_vlsi

Junior Member

Offline

Posts: 29
warangal

Re: Fourier analysis and DFT compare
Reply #14 - May 27^th, 2007, 9:29pm

hi sheldon and driveforce
can u tell me how u have got normaliser point is at 83rd hormonic �while i got it at 1st hormonic. fourier component �results �r shown below.
========================
Fourier Analysis `FOUR1'
========================

Fundamental frequency = 122.07 kHz.
Fundamental period = 8.19202 us.

Fourier components of V(OU) for the interval from 1.80798 us to 10 us:
DC = 498.416 mV.

Harm: �Absolute �Absolute �Relative �Relative
Magnitude Phase � � Magnitude Phase
� 1: �19.2405 uV � � -4.53968 Deg � � 0.000 dB �0 Deg <- normalizer
� 2: �8.87069 uV � � -151.694 Deg � �-6.725 dB -147.154 Deg
� 3: �64.5489 uV 96.2625 Deg � � 10.513 dB 100.802 Deg
� 4: �9.9571 uV -112.919 Deg � �-5.722 dB -108.38 Deg
......
508: �39.9502 uV 18.8854 Deg � � 6.346 dB �23.4251 Deg
509: �75.2377 uV � � -160.875 Deg � � 11.844 dB -156.335 Deg
510: �14.0832 uV 127.099 Deg � �-2.710 dB �131.639 Deg
511: �8.52414 uV � � -68.0349 Deg � �-7.071 dB -63.4953 Deg
512: �5.03811 uV 162.856 Deg � �-11.639 dB 167.395 Deg
Total harmonic distortion = 2.5702 M% (88.1994 dB).
RMS value of computed spectrum (excluding DC) = 494.52 mV.
RMS value of computed spectrum (including DC) = 702.117 mV.
Nonperiodicity (first/last point mismatch) = 0 V (0 %).

regards
venkats

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s.venkat_nitw

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