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Interpolation and power

Started by mkm10 6 years ago5 replieslatest reply 6 years ago437 views

Does interpolation change the power/energy of the signal...?

When I upsample a signal and pass through a unity gain anti-aliasing filter, does the power / energy of the signal remain same...? I am observing a decrease which relates to interpolation factor.

Does the anti-aliasing filter is expected to have the gain as interpolation factor..?  

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Reply by spetcavichFebruary 28, 2017

You will  need to scale your interpolation output by the interpolation factor...The gain is reduced by a factor of your interpolation

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Reply by Rick LyonsFebruary 28, 2017

Hi.  spetcavitch is correct.  Try this:

Generate a low-frequency sine wave sequence whose peak amplitude is one.  Upsample that sequence by four, by inserting three zero-valued samples in between each original sample.  Pass the upsampled sequence through a unity-gain FIR filter.  Make sure the filter's passband includes the frequency of the original non-upsampled sine wave and the beginning of the filter's stopband is less than the first image frequency within the upsampled sequence. (You must attenuate the spectral images within the upsamped sequence.) The peak value of the low frequency sine wave out of the filter will be be roughly 0.25 (one fourth the peak amplitude of the input sine wave).

If you don't like that filter gain loss of one over the interpolation factor (1/4 in my case), merely multiply your filter coefficients for four.

By the way, when performing interpolation the filter is not called an "anti-aliasing filter", it's called an "image reject filter."



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Reply by mkm10February 28, 2017

Agreed with Rick & Spetcavich..

Image reject filter gain need to be properly upscaled by interpolation factor.

Seems like this gain compensation is required only for image reject filter but not anti-aliasing filter ( used for decimation ). Am I right?

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Reply by Rick LyonsMarch 1, 2017

mkm10, to experience a sense of personal satisfaction it's better for you to answer your question yourself--either by drawing time-domain sequences on paper or by some software modeling. That way, what you learn is more likely to embed itself more deeply in your memory.  After doing that, you'll be ready to work this homework problem from my DSP book:

homework_2085.jpg

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Reply by LoganathanNMarch 1, 2017

Hi

Spetcavich & Rick Lyons both are correct if you are interpolating your signal by inserting zeros. If you are using anything like CIC filter for interpolaton, then you'll have pass band droop based on your Rate Change (R), No. of Stages(N). I mean droop as attenuation slope in the pass band region. To compensate this you need to design a Inverse Sinc Low pass filter to add slope gain based on your CIC response.


Thanks & Regards

Loganathan N