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Normalization of FFT Spectrum

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Dear Sir

 

I take FFT of my real time data that I collect from current probe. I successfully get the FFT spectrum. But my supervisor ask me to normalize the harmonic component present at 25 Hz in the FFT spectrum with fundamental component. Can you please guide me how I should do this task.

Also what is normalization and what are its benefits.

 

The frequency of fundamental component is 50 Hz.

 

Your attention and consideration will be highly appreciated.

 

Kind Regards

 

Urfee

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Urfee,

 

Normalization, when used in this manner, is the process of setting the reference component (the fundamental) to a magnitude of unity and scaling all other components by the same amount. 

 

One practical way of doing this is to find the magnitude of the fundamental component and divide all components by that value.

 

The major problem occurs if the sampling is not synchronous with the fundamental frequency. Then the energy of the fundamental is spread over several frequency bins and the calculation of the magnitude of the component is not so simple. 

 

What is your sampling frequency?

 

Please run your VI until you have some data shown on Data Graph 2. Stop the VI. From the Edit Menu select Make Current Values Default. Save. Then post that VI. It will have the data saved so that we can see it.

 

Lynn

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Dear Sir

 

I am using sampling rate 25 KHz and total samples collected is 100 K. In attachment, I have replaced real time DAQ with simulated signals so that you can run the vi. In simulated signals 50 Hz signal is fundamental while 25 Hz and 75 Hz signals are harmonics.

 

 

Kind Regards

 

Urfee

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Urfee,

 

Here is one way to normalize. Note that the dB mode must be off. Also be aware that if the sampling frequency was not a integer multiple of the fundamental frequency, this method would not work as well.  

 

Because you are generating simulated signals, it is not necessary to save the data as default in the graphs. The file size is 93 kB compared to 2.2 MB.

 

Lynn

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Dear Mr Lynn

 

Can we get the values in dB? And also I could not understand the benefit of normalization. Does without normalization, results will not be accurate?

 

Kind Regards

 

Urfee

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You can manipulate the data in dB units, too. The operation for this is different:

manipulate Ampl in dB.png

 

Because you are working in the logarithmic scale, when the units are in dB, you have to apply Subtraction instead of Division and Addition instead of Multiplication.

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tronoh wrote:.And also I could not understand the benefit of normalization. Does without normalization, results will not be accurate?

No, the data is accurate before and after normalisation as well. The difference is a human perspective. The data may be better readable after the normalisation. One can quickly see, how much is the attenuation at the questioned frequency compared to the value at the fundamental frequency. Otherwise, one had to do a subtraction "on the fly".

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Dear Sir

 

I have try to "normalize" the instantaneous current spectrum and instantaneous power spectrum but i could not do it. Can you please help me in this regard. My vi is attached.

 

Also can you please verify that whether my method to calculate instantaneous power is correct or wrong. (I measeure motor line current "I" and phase to phase voltage "V" both are at 50 Hz fundamental frequency, then I multiply instantaneous current with instantaneous voltage to calculate instantaenous power "VI")

 

Best Regards

 

Ifee

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The problem is to know what to use as a reference for the normalization. The image below shows an expanded view of the Instantaneous Current Spectrum with the display style set to show the actual data points. I also moved the frequency indicator wired to the Tone Measurements VI into the image. The frequency as detected is not exactly 50 Hz. Note that the data points in the spectrum are not symmetrical about 50 Hz. This is another indication that the sampling is not perfectly synchronous. The result is that the spectrum contains 11 points fro 49 to 51 Hz which are within 60 dB of the highest point.  If you want to normaize to the fundamental, you need to determine the total energy in the fundamental component. That probably includes the data points in that 2 Hz range or maybe slightly more.

 

Although you stated that you are sampling at 25 kHz, the latest VI you posted shows 8 kHz sampling.

 

Multiplying the voltage and current waveforms will give you instantaneous power - almost. If you are using a multiplexed A/D converter, then there is a small time delay between channels. That produces a phase shift that will introduce errors in the instantaneous power and other results like power factor. For example sampling two channels at 8 kHz means that each sample on one channel is 12.5 us apart. Consecutive voltage and current samples may be separated by half that much (assuming you are only sampling two channels). The phase shift at 50 Hz from a 6.25 us delay is 0.11 degrees. You will need to decide it that introduces more error than you can tolerate.  Faster sampling will reduce that. Using a simultaneous sampling DAQ device (which contains one A/D converter per channel) will eliminate it.

 

Lynn

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Dear Sir

 

My device is NI PCI 6281, I select sampling rate of 8 KHz and total colected samples 64 K, sampling mode continuous, terminal configuration Differential mode

 

1. For instantaneous current spectrum, I want to normalize with respect to fundamental component which is at 50 Hz.

2. For instantaneous power spectrum, I want to normalize with respect to fundamental componet which is at 100 Hz.

3. Minor error in phase shift of instantaneous power is acceptable.

 

 

Kind Regards

 

Irfan

 

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