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Nyquist Condition question.

Hi all, (1) I know the famous Nyquist Condition, f(t) with bandwidth B is sampled without aliasing if Fs> 2B. Today I read another thing called Nyquist Condition which says: for a continuous time signal x(t), take x(t) convolute with itself and then sample the obtained signal at Fs, ...

Re: Interpolation

On 2 Apr., 12:36, Randy Yates wrote: > dbd writes: > > [...] > > .How can a 'properly designed' decimation filter not anti-alias when > > .there is input signal content above the Nyquist frequency of the > > .downsampled sampling frequency? > > Dale, > > Here's an interes...

Re: Interpolation

On Wed, 2 Apr 2008 04:12:06 -0700 (PDT), Andor wrote: > On 2 Apr., 12:36, Randy Yates wrote: > > dbd writes: > > > [...] > > > .How can a 'properly designed' decimation filter not anti-alias when > > > .there is input signal content above the Nyquist frequency of the > > > ...

Nyquist sampling theorem

Hello, I read in the text book ("Digital signal Processing Principles, Algorithm and APplications" J. G. Proakis % D. G. Manolakis, page 30) that the Nyquist frequency (rate) is a double of the highest frequency of the signal. In the web, I learn that it is the double of the bandwith. Moreover ...

Re: questions raised by reading and thinking with possibly missing background

abariska@student.ethz.ch wrote: > > > Since Fs = Ts = 1, I don't see a difference between sinc(t+1/7) and > > > sinc(n+1/7) ? > > ... > You claim that the infinitely long sequence > > b[n] = sinc(n + 1/7), > > for all n, is linear-phase. That could be true. Do you have an ide...

Nyquist rate for sampling complex-valued data?

I (vaguely) heard that sampling complex-valued data does not abide by the Nyquist rate criteria, i.e., the sampling rate fs can go lower than Nyquist rate and it still can avoid aliasing and reconstruct perfectly... Is that true? Any theory behind it? Thanks a lot ...

Nyquist constrain and IQ represented signal

Hello, there is a question that bugs me for quite a long time: You can read about Nyquist constrain online, that to reconstruct all frequencies within a signal, it has to be sampled with at least twice the bandwidth _or_ maximum frequency. Maybe this _or_ is already the problem... Let's se...

Sampling Theorem history

It is generally credited that the Sampling Theorem is due to fistly the Mathematician Whittaker and Shannon and the Russian Kotelnikov. I have no doubt that Whittaker was first but was Shannon aware of Whittakers work? Also where does the Russian engineer fit in? What role did Nyquist play. We t...

Re: Interpolation

On Fri, 4 Apr 2008 10:58:49 -0700 (PDT), robert bristow-johnson wrote: (snipped by Lyons) > > possibly you're right. but i think the term is nearly universally > understood as Fs/2 (or z = -1 on the unit circle or pi in normalized > omega, but not "1" as stupid MATLAB scales it) and i...

Re: Questions about equivalents of audio/video and digital/analog.

On Sat, 25 Aug 2007 06:16:10 -0800, floyd@apaflo.com (Floyd L. Davidson) wrote: > > > > I guessed you would think it was correct. You can't sample at a rate > > equal to twice the frequency you are sampling. The wanted signal has > > collided with its image and you can't disambiguate them. T...

Re: Questions about equivalents of audio/video and digital/analog.

On Mon, 20 Aug 2007 22:14:45 -0800, floyd@apaflo.com (Floyd L. Davidson) wrote: > > source that you claim is authoritative and impeccable. Kindly go and > > read what it has to say on the Nyquist rate and come back and repeat > > that claim without blushing. Actually I'm betting you won't blus...

Re: decay rate of the spectrum?

Luna Moon wrote: > Hi all, > > If I have the signal not in closed form, but in form of some > collected data. > > The sampling(or collection) of such signal data points are very > costly. > > Thus we want to minimize the number of samples(data collection). > > Is there a wa...

Johnson Nyquist Noise

Hello All, I had a recent situation where I needed to write a paper explaining the why's and wherefores of Johnson noise. So if you are interested, the following link will take you to my paper. http://www.claysturner.com/dsp/Johnson-Nyquist%20Noise.pdf Any and all comments welcome. ...

I wonder if there is a spatial Nyquist sampling theory?

Is there a Nyquist sampling theory for spatial dimensions? Suppose point A to point B is about 1 mile, how many sensors I should place to get a fair estimation of the property of the whole range? ...

Re: Questions about equivalents of audio/video and digital/analog.

Floyd L. Davidson wrote: > Jerry Avins wrote: > > Floyd L. Davidson wrote: > > > > ... > > > > > Nyquist rate: > > > The reciprocal of the Nyquist interval, i.e., the > > > minimum theoretical sampling rate that fully > > > describes a given signal, i.e., ena...

Nyquist frequency in FFTs

Hello all, I noticed that all FFT routines transform a time array into a frequency array of the following form: F[0], F[n/2], real:F[1], imag:F[1], real:F[2], imag:F[2], etc.. Now the question is, why does "F[n/2]" (the nyquist freq) appear as the second term, and more importantly, what i...

Cycles/inch frequency, really confused, plz help!!!

Hello all, I am really confused with how people calculate the spatial feq values in FFT: Assume I have a continuous signal f(x), in spatial domain. I need to know at what freq (cycles/inch) the flactuation is the most dominant (highest). Assume that freq is f_d. Firstly I sample it wit...

Re: A DSP Decimation Riddle

> When is decimating by N not equivalent to decimating by 2*N followed > by interpolating by 2? I think, except for a handful of pathological cases, any time bandwidth > = Fs/4N. For example, try it with a sine wave (NOT a cosine wave) of frequency Fs/4N. Decimate by N and Nyquist is sti...

Need Phase-Lead filter.

I need a digital filter or sequence of digital filters with the following response: Amplitude flat across all frequencies up to the Nyquist (folding) frequency. Phase starts at 0 degrees at low fregs linearly increases with frequency until it is 180 at the Nyquist (folding) frequency. ...

choosing a sampling rate lesser than nyquist rate(sub nyquist rate)

Hello, I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) and dc component.The signal is very pure and SNR better than 60 dB. I have to sample it in sub Nyquisit rate(lesser than 1600k). What sampling rate should i choose so that there no alaising. I cannot chose higher samp...

Re: downsampling -> FFT -> upsampling

> Consider your idee fixee: if every second sample of a set of valid > samples is discarded, the result is still a set of valid samples. How > many times in a row would you apply that theorem? Why stop there? I'm not saying it's "the same". If I said that then I expressed myself wrong. What...

Low freq "analog" of Nyquist? ( possibly naive question )

I understand Nyquist specifying a minimum sampling rate to determine the high frequency component of a signal. What happens at at the other end of the spectrum? I.E. Is there a minimum time window required? E.G. If the signal has a significant 1 Hz component and sample window was .1 sec...

Low pass filter at half Nyquist

Hello, I'm currently using an FFT to zereo out all the frequences above half Nyquist for my application. It makes perfect cutoff, but I have to use buffers and the old overlap/add to remove clicks. My question to you good folks - is there a clever 'trick' to cut frequencies off above this s...

Nyquist Sampling

I'd like to ask a couple very basic questions. Being hands-on rather than mathematically-focused I'm trying to visualize sampling in a project I'm planning to start. 1. By sampling say a 3.1 kHz band-limited voice channel at the Nyquist rate am I guaranteed to capture *all* the information...

What Nyquist Didn't Say

I've seen a lot of posts over the last year or so that indicate a lack of understanding of the implications of the Nyquist theory, and just where the Nyquist rate fits into the design of sampled systems. So I decided to write a short little article to make it all clear. It's a little longe...

Normalized frequency (freqz function)

Lets say I have a filter with a cutoff at 100Hz and my sampling rate is 1kHz. This means my cutoff is at 0.1 in normalized frequency terms. But it seems that the matlab freqz function plots my cutoff as being at 0.2, because it defines normalized as being relative to the nyquist. Is this not rea...

fundamental question

A very basic question: Take two properly sampled signals (more than nyquist). Now I mulitply the two sample streams. From a continous time view point it is easy to see that the product could have frequencies for which the initial sampling rate wouldnt be enough. So in any DSP system is one ...

Re: Regarding sampling.

Ted wrote: > Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling...

Does anyone have any reference to sampling distortion?

To all you DSP mavens out there. I am looking for some references to distortions introduced by sampling = errors, especially sampling close to the Nyquist criterion. In all the = literature I have seen, reconstruction of a waveform is guaranteed if the sampling = meets the Nyquist criterio...

Re: CW detection on DSP

Ron N. wrote: > On Aug 1, 9:16 pm, Jerry Avins wrote: (snip) > > You know it's CW if it has no sidebands: i.e., it has a line spectrum. > Morse code modulated CW does have sidebands. The > bandwidth required for typical human demodulation is > around 2 to 4 times the WPM, although ...

Re: is FFT always approximate?

Michael wrote: > If I have a time signal which is periodic, and I use FFT to obtain the > spectrum, which should be discrete, will this FFT procedure be approximate? > I am wondering about this because I've heard that FFT is only an > approximation to the true Fourier transform... There...

Re: Is a signal containing random numbers White Noise?

just to be clear guys, truly "white" noise has infinite power, and i doubt that Chris's random numbers have infinite variance. random number generators usually output uniform PDF pseudo-random numbers that are "virtually" independent of each other. these numbers are hypothetically "sampled"...

FIR gain

I have an FIR filter with the system equation y[n] = 0.25x[n]+0.5x[n-1]+0.25x[n-2] which gives an impulse response of h = [0.25 0.5 0.25] without resorting to Z-transform analysis, how can I work out the gain of the filter at DC and at the half nyquist frequency? I think the gain of the fil...

The Sampling theorem

This is due to Whittaker E. T. Whittaker, On the functions which are represented by the expansions of the interpolation theory, Proc. Roy. Soc. Edinburgh 35 (1915), 181-194 http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Whittaker.html and to Kotelnikov V. A. Kotelnikov, ...

Re: Help: How to design the audio pre-emphas(J.17) filter.

Randy Yates wrote: > Since you have the s-domain response, I would use the binlinear transformation. And the resultant pre-emphasis filter will have (1) infinite gain at nyquist (not a good thing) and (2) due to frequency warping, it probably won't have an ideal response. I fought with...

Re: Oversampling vs. nr. Bits

I'll try to answer from an analog guys perspective. 12 bits gives a quantizing noise floor of about -72 dBc. This Q noise is spread across the entire Nyquist bandwidth. If you double the sampling rate, the Q noise floor is still -72 dBc but the Nyquist bandwidth has doubled so while the tota...

Question about FM

I am trying to implement FM algorithms for computer music applications. The language I'm using (Nyquist) has a primitive FM oscillator called fmosc. I want to use modulators in series which is a very common technique in some Yamaha synths. In pseudo code it is the composition fmosc(fmosc(osc())...

Re: basic DSP example & my confusion

Thanks, Jerry, Tim, You've been quite helpful. First let me say that I understand what he's trying to show - that undersampling can alias a signal down to baseband, or at least a lower frequency. I'm trying to use this book though to understand a few related things that relate to my work. L...

Re: Halfband FIR design with alternating zeros

in article 5JqdnR5udeMrETXfRVn-vw@rcn.net, Jerry Avins at jya@ieee.org wrote on 06/09/2005 14:38: > Middle coefficient non zero, but all other odd-numbered coefficients. > Round-off errors usually cause computer programs to return very small > numbers instead of zero. Ignore those. also,...

sampling a perfect sinusoid at Nyquist rate?

Let's say you have a perfect sine wave at frequency w. According to Nyquist, in order to be able to recover the sine wave, you need to have a sampling rate of at least 2w. So if you decide to sample at 2w, you end up with 2 samples for each cycle of this sine wave. If you sample at the peaks ...