[SOLVED] Is there any Upper limit of sampling frequency

[kripacharya]

We where talking about time domain. For representing an analog signal as digital time samples we should sample and then filter.

Im not sure but maybe you're right.
Filtering is a convolution of signal time samples with impulse response of a filter. Direct formula requires much resources, so it is frequently implemented through FFT.
FFT of time samples of period T gives the spectrum in band 1/2T.
To cut off higher frequencies we apply some kind of windowing the spectrum. For example, rectangular.
The rectangular is FFT (spectrum) of filter impulse response of sin(x)/x kind.
So FFT-windowing-IFFT (for restoring time samples is equivalent operation to filtering.

no no, windowing is put after sampling but before fft calculations. i think hanning or gaussian is better. rectangular means no windowing

 

[Mityan]

So your windowing is not the same as filtering and it cannot help to remove frequency components higher than some given value. Filtering is needed anyway I think.

 

[kripacharya]

So your windowing is not the same as filtering and it cannot help to remove frequency components higher than some given value. Filtering is needed anyway I think.

it is not my windowing. Windowing is standard technique for doing FFT on discrete samples. To get frequency components of input signal upto - example 100Khz - we can sample it with 200 Ksa/ s speed. Then multiply all samples with window function, and do FFT. Then the nth bin will contain the power of frequency component at 100Khz. No need at all for any filtering

i think difference in our opinion is because you are trying to maybe display an analog time signal which is exact replica of original signal - like in oscilloscope, but all others are only trying to find out what is the frequency components of the input signal - like in spectrum analyser. yes ?

 

[permute]

There are a lot of conflicting ideas throughout this thread.

This is square wave. When process the sampled data from ADC you always assume that between samples the value of discrete function remains the same as that sampled at the last moment.

For bandlimited signals, values between samples can be interpolated using a weighted sum of all samples. This is what allows reconstruction to work without error in the bandlimited case. There is no requirement that anyone assume the ADC sample remain constant between samples.

So your windowing is not the same as filtering and it cannot help to remove frequency components higher than some given value. Filtering is needed anyway I think.

Windowing is a similar concept, but slightly different reason. the FFT takes N points of data, and produces N samples of the spectrum. These are exact, but only for the data used for the FFT. Windowing determines how content between these N samples of the spectrum affect the N samples of the spectrum. Or, alternatively, describe how the N samples of the spectrum could be used to interpolate the frequencies between the N spectral samples.

This can have a similar function as filtering, as out-of-band content's effect on in-band content can be affected by the choice of window function. Though an iFFT of the windowed FFT would simply return the windowed samples which have not been filtered in the convolutional sense.

i think difference in our opinion is because you are trying to maybe display an analog time signal which is exact replica of original signal - like in oscilloscope, but all others are only trying to find out what is the frequency components of the input signal - like in spectrum analyser. yes ?

For the bandlimited case, these two would be the same. For anything else, you would need to state your assumptions and measurement methods.

 

[kripacharya]

Actually imho Nyquist criteria states that going from 2Mhz to any higher sampling frequency for a max 1Mhz signal will add NO additional information or improvement. Not even 1%

For the bandlimited case, these two would be the same. For anything else, you would need to state your assumptions and measurement methods.

it has from the begining been assumed we are dealing with a bandlimited signal. The confusion is that mityan contends that such a signal is impossible, and if we sample a signal at 2x the highest freq component (say Fmax), then even though we know it's max freq, somehow the samples obtained of Fmax - which will be 2 per cycle - actually represent an arbitrary signal whose components extend to infinity in the frequency domain, and not just a single sine freq at Fmax.

this is very hard for me to understand. i think i need refresher course in sampling theory and discrete fourier now.

 

[permute]

I do see the confusion over "Windowing" as well. Mityan originally seemed to be referring to a method that is similar to filtering where the FFT results are scaled and then an IFFT is taken. This would be similar to filtering, though not exactly the same. The method would perform a circular convolution instead of the normal convolution.

However, in the context of FFT's, windowing more often refers to a pre-scaling of the input samples before the FFT. this has the effect of filtering the FFT -- blurring spectral peaks while reducing the effect of distant frequencies.

The difference between the two is the difference between multiplication and convolution -- multiplication in the frequency domain results in convolution (filtering) in the time domain. Multiplication in the time domain (windowing) results in convolution in the frequency domain.

 

[kripacharya]

oh good !! so maybe i can skip the refresher classes for myself, and suggest them for Mityan instead ? ;-)

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... A Nyquist frequency of 1 kHz would refer to a stationary 1 kHz sine signal, thus no additional information is revealed when sampling it above 2 kHz, as rohitkhanna mentioned....

i notice that both FvM and Rohitkhanna had a similar view to mine in earlier postings

 

[Mityan]

I do see the confusion over "Windowing" as well. Mityan originally seemed to be referring to a method that is similar to filtering where the FFT results are scaled and then an IFFT is taken. This would be similar to filtering, though not exactly the same. The method would perform a circular convolution instead of the normal convolution.

I think in practice filtering is always a circular convolution. Look, when you have a buffer of input samples of length N at a known rate, and have a filter impulse response of length M, the convolution result will have length N+M-1. If you preserve the input rate for these samples, you will have an incorrect filtering result. Adjusting the rate seems to be of great headache - it depends on buffer length, filter length... So N samples at input - N samples at output - circular convolution is wise decision.
And FFT-multiply-IFFT is not similar to filtering - it IS the EXACT filtering.

Windowing before FFT - this is not the filtering, this is just for spectrum beauty. The cutoff of signal in time domain gives us the spectral components that should not be there, and we know it, so we are trying to smooth them by windowing.

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oh good !! so maybe i can skip the refresher classes for myself, and suggest them for Mityan instead ? ;-)

i notice that both FvM and Rohitkhanna had a similar view to mine in earlier postings

I cant say anything about FvM's point of view, but Rohitkhanna doesnt understand anything in sampling theory at all, and his view is similar to yours? Congratulations, brother.
If I should return to school, you first say where is my mistake? Maybe I could not give an exact detailed explanation, but refer to Walt Kester's ADC book chapter 2 and you will learn why F_sampling = 2*F_upper is not enough.

 

[kripacharya]

I cant say anything about FvM's point of view, but Rohitkhanna doesnt understand anything in sampling theory at all, and his view is similar to yours? Congratulations, brother.
If I should return to school, you first say where is my mistake? Maybe I could not give an exact detailed explanation, but refer to Walt Kester's ADC book chapter 2 and you will learn why F_sampling = 2*F_upper is not enough.

relax dude, just having a little fun here.

btw kester also says that 2x is enough in theory. But he (like everyone else) adds that oversampling by some margin has some practical benefits in certain applications & implementations, and in the presence of noise, jitter, and various inadequacies of real A/D converters. Thats all.

lets close this thread now, shall we ?

 

[Mityan]

Deal.
For sampling the exact oscillator sine wave fs=2*f will be enough.

 

[FvM]

Most confusion in this thread is created by not distinguishing systematically between basic signal theory law (e.g. Nyquist theorem) and practical signal processing requirements. In this case, there's also theoretical problem.

fs = 2*f doesn't work. If you e.g. sample a continuous sine wave exactly at the zero crossings, you get all zero samples and no frequency or amplitude information. fs > 2*f is generally required.